cheapest way, wire it up try a set of known good tubes, simple way, get a tester, but the price? well put a pound of sand into the lube, and bend over.
the nasty tar thats leaking out, unless its really really old is likely not PCB, a look on the ballast will usually say does NOT contain PCB ( look hard usually really tiny writing in the corner of the sticker ) , if its unmarked well then sneak it into the garbage or be responsible and find a proper bin for it, some recycle yards will take a few from home owners, but the big shops pay to dispose of those.