shouldn't be a problem for RCA....if it was some odd brand you might have to worry..
if the given RCA setup codes don't work, try GE or proscan.
How'd the other remote break? buttons stop working? sometimes you can pop them open and clean the contacts on the circuit board with an eraser (where the rubber button touches it to complete the circuit), and that will fix the problem.. too much conductive dust shorts out the contact.
otherwise, yeah, a cheap one for all remote should do it...keep the receipt just in case