Regarding the assumption of Classical Linear Regression Model For the given model $y = x\beta + \varepsilon$, the four assumptions would be


The model is linear in $x$ and $\beta$, also additive in $\varepsilon$
The conditional mean of the error terms are zero (i.e. $E[\varepsilon|x] = 0)$
$Var[\varepsilon|x] = \sigma^2I_n$
Exogeneity of $x$ (i.e. either $x$ is fixed or independent of $\varepsilon$)


My questions is that in the case of the following situations which assumptions have been violated.

Case 1. $E[x'\varepsilon] \neq 0$ [I am not sure whether this implies the second or fourth assumption has been violated]

Case 2. $Cov(x_i,\varepsilon_i) \neq 0$ [I suppose the third one has been violated but could it imply the violation of other assumptions?]

Any help will be greatly appreciated.
I  assume that x is a scalar.( but argument is similar if it isn't).  

They both violate condition 4) because they both say that x, the regressor, is not independent of $\epsilon$. Case 1 a theoretical statement about the regressor and the noise term. Case 2 is an empirical statement about some of the  actual regressor data and the noise term.   If you want a nice intuitive explanation of econometrics ( not a standard textbook exposition ), I highly recommend Peter Kennedy's text. I think it's called "econometrics"but I'm pretty sure he only wrote one book so you can google for him on amazon.