I have a 95 buick rivera (supercharge) the signal lights on passenger side work but the running lights don't. I have switched the bulbs from one side to the other but that side still doesn't work. What is wrong?

If part of the system is working, then you probably have a ground on that socket. What you don't have is power when you want it. With a test light, trace back on the power wire for the circuit you need until you find where the open is. You can begin with a thorough inspection and see if you find anything obvious. Good luck!