Theres why the keys showing as invalid; it sounds like an HP key, tied to HP hardware (mainboard). Normally would have expected the key to revoke if you moved the disk into a new mainboard, but have seen strange things like that some times.
migrating to the ssd probably didn’t include the original recovery partition, not that I’d expect that to help in this state.
Rock and hard place I’m afraid 🙁
Cheapest (and kinda legal) option is probably purchase widows for this machine and install. You should be able to get OEM version fairly cheap from say pbtech. Just purchase it with a new drive as well (have a look at raid 0 ssd array…. Mmmm speeed).
Edit: (from memory, and I’ve been drinking) if you’re a student you may be able to get reduced costs if you can provide your tertiary details.