About three weeks ago I purchased a 1983 Fender Strat. It's been working amazingly since then but tonight I attempted to practice with my bassist and all I could hear out of the amp was buzzing everytime I touched the strings. I know its not the amp or chord because I used my other electric.

Could the wiring have gotten loose? How much does that usually cost to fix?
quite possibly its the wiring gone loose but i'd also check ur switch.
its a vintage so i dont even wanna bother trying to troubleshoot with you...cant say for sure but i do worry since you just got it

it does sound like a d/c ground though...as for a quote it depends, make sure you tell them its a vintage though...might cost you a bit more but they might also take special care of it
1983 isn't vintage. No doubt, a very nice guitar, and that the wiring has just gone a miss. If you know what you're doing, take the scratch plate off and have a look, if not, take it to someone who does.