Seriously, you need to replace the old electrolytic caps. They cost a lot less, and are easier to obtain than, a power transformer. Even the big multisection cap cans. You can use individual single unit caps to replace them. But don't just solder the new caps across the old caps, that won't protect you if the old caps short out (this is the failure mode to fear, this is what will ruin the power transformer). I've taken a hacksaw and cut the old can cap just above the crimp bulge (this is where the rubber gasket seal is housed), removing the old cap can and guts, and Ive drilled small holes thru the gasket and passed new cap leads from above to the terminals below. Some people will go to the trouble of carefully tucking the new caps inside the old can (after the guts are pulled out (nothing overly toxic, but don't eat it and wash your hands afterwards)) but I've just had the new caps out in the open (but take care to be sure they can't flop around and short out to something).
Flybacks and yokes and CRTs are also hard to find replacements for, so we also change out the caps around them as well.
I know, as a kid you probably have no real money to get this stuff, but you risk ruining hard to obtain parts.
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