Having experienced many dead starters on my car, I can tell you if your lights aren't shutting off or dimming when you turn the key to START, then your starter is probably not engaging.
Assuming you have at least 9-10 volts with your key in RUN, then you should have the bare minimum amount of battery power required to crank the starter.
You may be right on the money as far as the relay is concerned. Your high-power relays are under the hood. Lift off the cover that says "Maxifuse/relay center" and you'll see them. Check any fuses that are marked "starter relay" as well.
2007 Pontiac G5
1999 Pontiac Grand Prix GT - Stock engine ate transmission.
1997 Pontiac Bonneville SE - Cammed engine ate transmission.