have a look under the playfield where the suspect lamp holder/s is, see if a related wire nearby has for instance a blob of solder causing a short?
Check the solder tab isn't touching anything other than the wire soldered to it. If you're unsure take some clear pics and upload them.
how confident are you with a multi meter? assuming you have one.
Search Bally Pinwiki and it will have numerous manuals you can check out that will have parts used in your machine.
https://www.pinwiki.com/wiki/index.php?title=Bally/Stern
Regarding humming, which appears to 'noise', with the machine off, try unscrewing the sound/speech board from the ground mounts, letting it hang and being super cautious the rear isn't touching anything, you could put some cardboard behind it, or with it on and one screw holding it in place, undo that one screw with one hand, holding the speech board in the other, pull it ever so slightly from the mounting points and hear if the humming is reduced or even gone?