Start with small squirt of wd 40 on all the outer cable ends you can see. Work the shifters and cables while pedalling.
Might be enough. If not, same for shifters and derailleur.
It didn't wear out or go out of adjustment when it was sitting around.
Start simple. Small amounts of wd40. It shouldn't be dripping down anywhere but all of it wicked up into the cable ends.
If that doesn't work it's replacement parts.