Hello.
I was trying to move my Windows 7 partition to free up space for Linux Mint and when I was moving my Windows 7 partition using GParted, I accenditaly cancelled in the middle of the resizing process (I wish I didn't), and now all my files are gone.

Do you know how I can recover my lost files? I don't want to pay $300 for a data recovery service.

Photorec can recover deleted files from a damaged partition. They will lose their filenames however.

Also try using losetup to create a device at the old and new partitions. Enough of the filesystems maybe present to either mount, or use photorec to recover files. Another program testdisk may be able to repair lost partitions. A lot depends on whether the before and after overlapped.

Here is a link to a live disro containing both. You should clone your drive with dd or ddrescue onto an external drive and use the recovery tools on the copy image file. Then you can start over from a new copy if you make unreversable changes.