First, consider that the Windows install might be broken (rather than the hard drive) or just configured for a different set of hardware, thus Windows is rebooting (or BSOD'ing but set to automatically reboot) since it is not recognizing your machine's hardware. (Windows doesn't take too kindly to hardware changes) - it might not be a hardware problem.
If you can get the hard drive recognized and mounted by a Linux system, then just copy data off it; otherwise, try ddrescue, TestDisk and Photorec.
ddrescue is a raw disk imaging tool that "copies data from one file or block device to another, trying hard to rescue data in case of read errors." The application is developed as part of the GNU project and has written with UNIX/Linux in mind.
TestDisk is powerful free data recovery software! It was primarily designed to help recover lost partitions and/or make non-booting disks bootable again when these symptoms are caused by faulty software, certain types of viruses or human error (such as accidentally deleting a Partition Table). Partition table recovery using TestDisk is really easy.
PhotoRec is file data recovery software designed to recover lost files including video, documents and archives from hard disks, CD-ROMs, and lost pictures (thus the Photo Recovery name) from digital camera memory. PhotoRec ignores the file system and goes after the underlying data, so it will still work even if your media's file system has been severely damaged or reformatted.
If the hard drive is faulty, you probably will want to create a disk image and operate on it instead of directly operating on the hard drive.