I have central air and heat, with a Nest thermostat. My system has Y, G, R, C and W wires coming out of it:

which are wired into my Nest like so:

In between, there is a splice where the C wire is spliced with electric and another wire runs from that splice back to the C hookup:

And then the other wires are spliced with a new set of the same color:

The heat and cooling work fine. I just can't get the fan to run on its own. What could be at fault and how can I diagnose it?