First things first... the BIOS tells Windows how many of what kinds of drives you have, not the other way around, so when you say "Windows isn't recognizing the HD, so it doesn't show up in the BIOS" that's completely backwards. If it shows up in Disk Management, than windows is seeing the drive just fine, Being you say its Unallocated, just right click on the Unallocated partition of your disk and choose format. Once it has a useable file system it will appear in your My Computer.
Secondly, you say "and now everytime I boot it says, "Non-system disk, press any key to reboot..." I'm assuming the comp was working fine until this error came up? Again.... Recheck your boot order as you were instructed before. If your SSD is Primary Master and set as main boot device, than either the SSD has failed, or you have somehow lost your MBR (Main Boot Record) Recheck all your connections before you go any further, replace cables, test with other drives. Make sure you ground yourself so you don't zap anything with static.