It won't damage anything at all. If you intend to slave your old Hard Drive in your new PC, alongside a new Hard Drive, then it is fine.
This way, you can install the operating system on the new hard drive (or boot into the pre-installed operating system on the new hard drive), and simply access the files you have on your old drive in windows. When you add new drives to a PC, windows will automatically perform a check on the disk, or a CHKDSK to make sure that damaged sectors are repaired.
The only thing which connecting your old hard drive to the new PC will do is potential infections from viruses, but this applies with all storage mediums. Having said that you should make sure that your old drive is free of any viruses and it's always a good idea to perform a check disk manually if not let windows perform it automatically.
|Desktop PC| |Macbook Air 13" (Mid 2013)|
|Windows 8.1 Pro (x64)| |AMD FX 4100 Black Edition 3.6 GHz @ 4.0 GHz OC| |Arctic Cooling Freezer 13 PRO| |Gigabyte Nvidia GeForce GTX 560 Super Overclock 1GB| |ASUS M5A78L-M/USB3 Motherboard| |Samsung 840 Pro 256GB SSD SATA III HDD| |Kingston HyperX 8GB PC3-14900 DDR3-1866| |OCZ ModXStream Pro 700W Modular PSU| |NZXT Vulcan Micro ATX Case|