RV air conditioner (and it always helps to know make and model) doesn't use a Start Cap on the Fan. The value of the Fan Run Cap will be the lower of the two. Say 5-10 mfd for Fan and 35-40 for Compressor. Compressor may/may not have a Start Cap in addition to Run, but will always have Run.
A new or known good Fan Cap sounds like a pretty safe bet to begin your troubleshooting. If it wasn't running up to speed, it could also cause the evaporator core to freeze up.
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB