Data recovery using a disk enclosure

My old HP Pavillion laptop crashed. It had Vista Home Premium 32bit. I now have a HP Mini running Windows 7 Home Premium 32bit. I need to get my files from my old HDD running Vista. I purchased a Gigaware Hard Disk 3.5 enclosure and placed the drive, which is a Western Digital ATA drive in the enclosure. Windows 7 sees the drive if I go to Disk Management, but it says it's unknown and wants me to Initialize it which will basically wipe the drive.

My question is does anyone have any suggestions on how I can get my files from my old HDD running Vista using my new laptop running Windows 7?

The drive shows up, but it doesn't recognize that anything is on it? as if it hasn't been formatted or anything.

The first thing I would suggest is to post a screenshot of the Disk Management tool. this can be found by typing "Disk Management" into the SearchBar.

You can also try using a recovery tool like Recuva to try and find the lost files. As long as they aren't overwritten, Recuva can restore them: Recuva - Undelete, Unerase, File and Disk Recovery - Free Download