I will add a closing note. It turns out when the hosting company copied the files from my old C drive into a folder on the new one, they missed some directories. So they didn't copy the data directory I needed. When I had them attach the actual old C drive so I could take a look myself, I found the files right where they were supposed to be, and got everything up and running again.
So it goes to show, always double check the source material yourself
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I now know a lot more about MySQL files and the differences between MyISAM and INNODB thought
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