if that were possible, everyone would be doing it. the xbox 360 drive isn't a traditional SATA drive, it's manufacturers implemented a special power interface and each drive has a alphanumeric "key" that needs to match the console's other internal parts (i.e. the mainboard) in order to work. even if you could get the drive to read disks when installed in a regular PC, which I don't think is possible anyways, you still wouldn't be able to play games or do much of anything. the xbox 360 isn't a PC, and vice versa, so it just won't work.
as a side note, 360's are fairly cheap if you're not looking to buy a brand new console. i bought an elite off ebay last week for $75.