Retrieving data from my old primary hard drive.

Hello, I have read the forums and there have been posts about this but none of the solutions work for me. I had a computer whose motherboard and CPU died. I bought a new computer. I am now trying to access the data from my old computer's hard drive. I have done 2 separate things. First is getting the external Hard Drive bay and using the USB plug to attach it to my new computer and access the old hard drive. After that I tried physically installing it into my new computer. Both options resulted in my computer correctly identifying and recognizing the hard drive, but if I try to access it in any way, I am immediately prompted to format the drive in order to access it. This obviously is a problem for me, as I want to get the data off the hard drive and formatting would wipe all data thus defeating the whole purpose of me accessing the drive at all! My OS is windows vista home premium 64 bit, any help would be greatly appreciated. Also the hard drive in question is a SATA Western Digital 320GB and was the main and only hard drive on my previous computer (using windows vista home premium 32 bit), it was not a spare or anything like that.

The OS on the old system was Windows Vista Home Premium 32 bit. The file system I am not 100 percent positive but I feel like it was NTFS? Or something like that...