It's likely that the quote you got assumes that the drive itself works, and all they're charging for is copying to another drive, or to CDs/DVDs.

For a drive that doesn't run on its own, the fee usually is at least $100 to see whether anything's recoverable, plus whatever they negotiate for actually doing the recovery.

If you think the drive itself is okay, you could get a USB box and put the drive in it, plug into a USB port on your own computer, and copy away.

USB boxes, the last time I looked, were available for around $30 - $40, and probably for quite a bit less if you do some shopping; and having one on hand can be quite handy if you need to transfer stuff to another drive - before or after the drive has been in your computer. Most of the boxes snap together pretty tightly, but if you work at it a bit you can open them back up to put a different HD inside.

John