Q:

How to explain truly emotional ghosts?

No, not like that!!! 

The Oxford Dictionary defines:

Ghost as "an apparition of a dead person which is believed to appear or become manifest to the living, typically as a nebulous image". Basically just an image.
Emotions as "A strong feeling deriving from one's circumstances, mood, or relationships with others".
Feelings as "An emotional state or reaction". which is actually a circular definition and not very helpful!
Sentient as "Able to perceive or feel things".

A more Biological-centred definition:

"Emotion, in its most general definition, is a neural impulse that moves an organism to action, prompting automatic reactive behaviour that has been adapted through evolution as a survival mechanism to meet a survival need."
Edit - As I understand it, Our current understanding of emotions, is that they are related to chemical reactions in the brain that could reach down to the quantum level. 

The Oxford Dictionary definition of a ghost is fairly static and boring. Using popular science fiction which has evolved from more ancient folklore, we can consider a ghost to be anything from; a wispy image, to entities that are stuck in a repetitive action cycle with no interaction with the living world (think scary repetitive sequences replaying the moment of horrific death), to messenger guide type ghosts who helpfully point people in the right direction, to a fully interactive spirits/astral projections/lost souls/ even transferred consciousness's with all the memories of the Deceased/Original person. These interactive 'entities' AKA 'ghosts' can interact with the Living world and react to outside stimuli (think, Casper, etc). 

QUESTION: 

If emotions are based on chemical and neural reactions inside a physical brain, and if no physical body is involved or the connection between the consciousness and physical brain is lost, how do I explain that my ghosts/ spirits/ lost souls/ transferred consciousness's are aware and have real genuine emotions? 
Edit - If, our current understanding of the physical brain does not allow it, what alternate theories on how emotions and consciousness are formed would allow ghosts to have an active and sentient consciousness?

I figure that they would be able to remember how they may have reacted to any similar situations, and even mimic those emotions. But I'm having trouble deciding if and how they would truly feel or if they would just be going through the motions? Would they be able to feel emotion about new experiences?

Edited Note as current scientific knowledge does not accept ghosts, please take a pinch or two of salt when considering answers. I'll accept alternate theories but am hoping for as realistic an approach as possible.
Note I'm not asking how to create a ghost which was a very interesting question I linked above. I'm focussing just on how to make it feel emotions.
Note I'm not asking about Artificial Intelligence having emotions as that would be too broad. I'm focusing on incorporeal entities with a living, human-body origin/backstory. 
Note for the sake of clarity, answers should consider a transferred consciousness as a 'ghost' from the moment of the copies 'creation' to the moment of 'implantation' into a new living body. Any interaction this consciousness may have in a technological environment, via computers or holograms etc., should be considered the equivalent as on the ghostly plane. Examples 'Tron' would be ghosts, 'The Sixth Day' would not be ghosts. 'Avatar' would not be ghosts either (The 'Avatar' example is actually a bit complicated and I have another question lined up about possession :) ) 
Note Also, I'm NOT asking how much tech is needed to go about transferring a consciousness. Answers to that last question focused mainly on the amount of computer processing power needed and not if and how the copies would be able to feel and interact.

Image source: Picture is from the movie 'Bedazzled' 2000 taken from the Dismantled Possessions Wordpress Blog.  

A:

The best explanations for ghosts and/or ghost-like creatures (GLCs) I've seen in literature tend to say the GLCs are one of two things:

Not actually a creature/being at all, but just some kind of "emotional/psychic residue" left over from an event at that location. It may look like a person, but it is more like a film of a person -- it maybe can play back an emotional event or even an emotional state, but it isn't really alive or aware in a spiritual/emotional/cognitive sense. I call these "emotional after-images"
It is the soul/spirit/mind/energy matrix/non-corporeal leftovers after a person has died. Rather than passing on to oblivion/heaven/hell/etc. the spirit remained behind. Most literature tends to link these GLCs to either people who died violently (the stereotypical murder victim who's body was never found) or people who failed to complete some sort of capital-E capital-T Epic Task. The ghosts who stay behind to protect a loved one fit this sub-category. I call these "tortured spirits."

Many more detailed variations exist, but they tend to fall into those two broad categories, emotional after-image or tortured spirit. (This ignores categories of other non-corporeal beings that may appear to be ghosts or GLCs, but are not.)
As for the "scientific" explanation, we cannot provide one because science has so far been unable to even confirm the existence of GLCs in any reliable, scientific, peer-reviewed way, much less explain what they are. At least not in the real world. In fictional worlds, it's up to the author to decide. Is it a soul? Is it some sort of aetheric residue? Is it electrical energy akin to static electricity? Is it some sort of quantum energy state caused by the manner of death or by extreme emotions? It could be any of those. Or all of those, if your setting allows.

A:

Well. What if how 'we' define emotions is 'biochemical reactions in the brain', but in your world it's not just the physical?
Let's take Eastern Mysticism for an example. Instead of just the physical, each person has multiple bodies, coinciding in our lived reality: 

The physical body
The emotional body
The mental body (ie. the mind)
The spiritual body
The soul

Now, there are quite a few different views on this. The 7 chakras, 'hovering soul' theory, which is why yogis avoid cities and the tall buildings therein, the 4 bodies, and likely quite a few more I have yet to hear of.
If you were to decide that 'ghosts' are beings that shed the 'physical body' (kicked the bucket, pushing up daisies, etc) while being unwilling (or for any reason under the sun 'unable) to let go of their mental/emotional bodies? 
There might be an emotional trauma that binds them to this plane? Perhaps anger at their (in their not-so-humble opinion) untimely death? Perhaps an unfulfilled ambition that haunted their every thought in life?
As a nod to currently known science (and those who believe in these 'alternative realities'), let's say there is a feedback loop between the bodies. Strong emotions affect the mental and physical bodies. So, they would affect how we think, and perhaps tense the muscles and perhaps even cause the stomach lining to bleed? Affecting hunger and sleep? No problem with this theory in place!
So, you have a ghost that has emotions, memories (from the mental body), and perhaps some ghosts that don't? Perhaps their grip on these other bodies loosen over time? So if they don't 'pass into the life hereafter' before a certain time? They become mindless... whatever, apparitions.
This then opens the door to other mythos to go with it. Like hungry ghosts, Yuki-Onna, and any other mythological ghost/demon. 

