Hey everyone! Hope you can help me here.

Toshiba MK2565GSXN

I've plugged the hdd into another computer using a SATA to USB adaptor.
When it's first plugged in, it takes several minutes, but eventually the OS will recognize Partition one (HDDRECOVERY) as well as the space used and space free. It will also list that a second partition exists (listed as an unnamed drive in My Computer). This partition has all the data I need.
When I try to access either partition, the computer freezes. And not just My Computer; other running applications will stop working, especially any partition programs or data recovery programs.
When I remove the hdd, both partitions show up in my computer for a sec and I get two notifications saying that I need to format the drives to use them.

Any ideas?

First you have to try to clone this drive with non-windows cloning program.

What would you recommend for that?

Try ddrescue.

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A backup a day keeps DR away.