hmm, if its gas.. was the rat up top on the grill part or down low/underneath where the propane tank is?
at my old house there was a rat family in the backyard but I never found any evidence of them being in the grill. I killed them all via mouse traps and kept with the grilling. and I'm still alive..
for you, if it was up top I would just sanitize the grill and then donate it/sell it, as you will never be able to get the image of the rat on your grill out of your head. if you donate it you can write off the full price of the grill on your taxes. if it was underneath then I wouldn't make such a big deal. just sanitize it and cook steaks tomorrow.
also, invest in a corral/and or cover for your bbq. those are probably what saved mine, even though they were intended to keep the little dogs from peeing on the bbq.