You just joined. ALWAYS Post Year and Model of RV. Post Model of appliance if you can find it. This helps tremendously in geting people help. Think of posting My Ford Explorer does not start with no info on the Car. See how hard it would be to try and get help:).
Odds are the Capacitors are good. They just "jump" start the motor. So, if the motor runs on LOW and you switch to HI, then usually the motor will go to Hi because it is already turning. Unless you have a 12 volt tstat supply problem. The HI tstat wire is not sending the HI run 12 volt signal to the upper board. You will see a GL(lo) and a GH(hi) on the upper control board. The wire to each will have 12 volts dc positive depending on LO or Hi selected. So, the FIRST thing is to see if the GH wire has 12 volts when Tstat selected for HI fan. If it does, then open up the control board cover and check for loose or burnt wires. DISCONNECT 120 BEFORE YOU DO THIS. Doug