So, I recently picked up an old Schwinn Varsity, much to my dissatisfaction, and managed to talk down down the price enough that I felt it was a decent buy even with its shortcomings. (Those being mostly aesthetic problems)

The main issue I'm having with this bike is that the freewheel 'cogs' don't spin at all. It's like they're glued or something. With a pair of thick gloves I can apply enough hand-torque to rotate them, but it takes an inordinate amount of force for something that should freely spin with a distinctive click-click-click.

What do you guys think could be causing this? Is it a massive build-up of gunk and grease, maybe some plant matter or string lodged in the mechanism? Is it possible for something to lodge in there like that, or does this represent a critical mechanical failure that necessitates replacement of the entire freewheel? For reference, every single cog is stuck and none of them spin freely. I'm on the fence about spending ten bucks on a freewheel removal adapter, under the concern that maybe the freewheel isn't even salvageable. I may be mistaken, but I believe freewheels can't have their 'cogs' disassembled like modern cassettes can, right?

I'm a broke student and am desperately trying to save enough money to buy a proper Peugeot, which if possible will take precedence over fixing up this old Varsity. If any of you guys have experience with this in the past, could you render a broke kid any advice? If I can just buy the adapter, strip the freewheel off, and maybe soak it in some violent caustic acid (well, just mineral spirits) for a few hours and put it all back together to form a working bicycle, I'd be a very happy camper.

Thanks in advance!

P.S. Don't tell me to throw the entire Varsity in the trash or take it to the scrap yard to get some more money for the Peugeot. Yes the thought has occurred to me many times, but I'm not going to get rid of it even though it's made out of lead.