I have a Hampton Bay ceiling fan whose motor fails to self-start. The fan has three speeds. All three speeds work fine if I hand spin the blades, starting at low speed of course. The fan has a remote unit. Once I hand start the fan the remote allows me to change speeds up and down and turn off the fan. I understand that the motor capacitors are in a black module in the receiver unit of the fan. I am trying to figure out if there is a starting capacitor for the motor or is this module the capacitor that I need to replace to get the fan to self-start?

Sometimes fans have a bunch of capacitors in the same case with many wires coming out, and you have to replace them as a whole. This is actually referred to as one capacitor with 3 or more wires.

It's a Hampton Bay fan, though, so I would just take it back to Home Depot.

Not at all, just look at these forums. Even though they have one or two designs I like I would NEVER buy one.