Why are you reformatting the drive? Is it formatted in NTFS for Windows? If so, the Mac can read the files off the drive, which is what you'll need to do. Reformatting is a destructive process, so if you want the drive in a different format (such as Mac OS Extended) you will need to copy the files off to another location temporarily and then bring them back once the drive is reformatted. Since the Mac can read the old drive, an external drive formatted Mac OS Extended could be attached as well and the files moved over.
If you don't want to do that, there are some third party options that will allow the Mac to read and write NFTS drives. The downside is that it's more than a bit tricky to do, and the risk of things going wrong when writing is likely why Apple defaults to only reading the NFTS drives and not writing to them.
If you will need to use the drive on both Windows and Mac machines the one "common" format is FAT32. That has its own issues (including a hard and fast 4GB maximum file size) but either OS will read and write the drive without complaint.
I was told reformatting was my only option.
I tried doing copying the files over to my old HP (which has been cleaned and had basically every program removed) but now won't recognize the hard drive at all. I don't need to use the HP anymore, I just need to get the files onto my MacBook. I'll try switching them over using my desktop at work.
It's interesting the HP can't see the drive anymore. Does the Mac see the drive?
The HP should see the drive unless it's formatted as HFS+ (Mac OS Extended), as it can read FAT32 (and other FAT variants) and NFTS. And if it's formatted as HFS+ the Mac would have no trouble seeing it (though it raises the question about how the drive got into that state :-) ).
And, as noted, however it's formatted the Mac should see it--it just won't be able to write to it if it's formatted HFS+.
Interesting enough, I had one external drive hooked to a Windows machine that ended up with a corrupted NFTS filesystem that Windows blew up on each time I tried to access the drive on a Windows machine--but the Mac could read it without an issue :-) . So we got the data off on the Mac and then copied it back to a Windows network share (weird data recovery, but it worked so I wasn't complaining).
Since neither the HP nor the Mac sees files now, it sounds like the HP did something to the drive during that crash. If you don't have a backup you might need to see about possible Windows disk repair/recovery utilities first since it's very possible the data is there but the directory structure got blasted in the crash. Depending on the nature of the damage it's possible all of the data might be recovered, or at least a substantial portion of it.
Any recovery would need to take place before you format it. And, if possible, you'd like to make a bit by bit clone of the drive onto another drive and then try to work recovery there.
If you do have it all backed up (and are sure the backup is good) then, clearly, reformatting and starting over with restoring the data is going to be by far the fastest fix.