I'm in the middle of the same problem, but in reverse. The compressor was running but the blower quit whenever it wanted. We would turn the thermostat to "OFF" for about 5 minutes and turn it back on to "COOL".
This got it running again 99% of the time. I did find the "Fan Relay" was sticking. I ordered a new one and I'm waiting to install it.
Keep me posted on how you do.