If two variables are not cointegrated, can one still cause the other? For part of a project, I wanted to see if electricity consumption causes GDP in Colorado. I initially intended to follow the approach of Mozumder and Marathe (2007), who use a VECM approach, but that requires cointegration.

I'm not sure what to do now. I tried the Toda-Yamamoto method but my errors seem to be serially correlated...
Causality between time-series variables does not require the two to be cointegrated. 

First, cointegration requires that each series be $I(1)$. It is certainly possible for two $I(0)$ series to follow a causal relationship (or two $I(d)$ variables for that matter). 

Second, cointegration implies a long-run equilibrium among the series, which is not required for a causal relationship. A long-run equilibrium between two time series variables $x$ and $y$ implies that
$$y_t-a-bx_t$$
is a stationary process. In other words, if shocks are 'turned off', the values of $x$ and $y$ will converge such that $y_t=a+bx_t$.