Record Player Rescue Assistance Needed

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I've been asking the thrifting gods for a record player for a few years now.  I know that I could just go buy one, but that feels like cheating.  I kinda want one to just find me.

And I thought it had, late last week, when my co-worker was cleaning out his office and had one to give away.  It was a little bigger than I would have liked, perhaps, but I loved the story that it had belonged to his grandparents.  He knew that the radio still worked, but wasn't sure about the turntable.  To sweeten the deal, he even hauled it out to my car for me.

Sweet Husband eyed my find skeptically.  "You say you think it works?" he raised an eyebrow.

"Only one way to find out," I replied.  "Go grab a record."

As we hadn't actually owned a record player--up to this point, I suppose--our selection was limited.  Sweet Husband came back with Pretty Hate Machine by Nine Inch Nails.  As he slid the record out of it's sleeve, I couldn't help but be amused by the idea that this was probably quite different than the last record my co-worker's grandparents had played.

But the turntable was spinning, which was a good sign, and I was quite optimistic until we put the needle down.

Trent Reznor sounded like he had sucked the air out of helium balloon.

Obviously, the record was playing too fast, but there isn't a switch to change the speed.  Subsequent googling has also been no help, so I thought I'd put it to you all.

Does anyone know anything about old record players?  If so, is there a way to slow this one down and make it usable?  Or am I still questing for an old record player?