I'm glad you found the splice, I was starting to question myself.
Ok, based on what I'm reading you should be able to turn the fan switch to "on" on the tstat (thermostat) and the fan will run. It maybe that you have to have your furnace in a mode (heat or A/C) for the fan to work. You don't necessarily have to have it set so it cools or heat but, just in that mode/setting.
If not, we are back to
- bad tstat
- a break in the green wire from tstat to splice
- or a break in the blue wire from splice to furnace
Without a multi-meter, we will have to start swaping wires to eliminate the problem.
Let me know.