Are you sure that you copied the boot sector from the correct partition?

Boot using your linux floppy and run ``fdisk /dev/hda''. Press `p'. It'll show you your current partition table. In the boot column, you'll see one of the partitions will have an asterisk. This is the one that the computer will try to boot on startup. It's probably your Windows partition. Make a note of it.

Does /dev/hda2 appear to be the Linux partition that you want to boot from? If so, try setting it to be the bootable partition (you might have to clear the flag from the current bootable partition) and hit `w' to save and exit, then reboot. If not, try a partition that does look right. If you can get your machine to boot directly into Linux, you're most of the way there. In fact, that's pretty much a prerequisite to get dual-booting to work.

Once you get Linux booting directly, boot off of your Linux floppy again and set the bootable partition back to what it was before. Then perform the steps you already listed again, replacing /dev/hda2 with whatever partition you set as bootable that got Linux to boot directly.

That should work. You might have trouble getting Linux to boot directly at all. You'll then have to look into getting your Linux boot loader (likely lilo or grub) fixed. That can be complicated, but this should at least point you in the right direction.