You've basically built a new computer; generally that means a new license. There's still a few things you could try though:
- Undo your changes and remake them individually with a little bit of time between each change (this is basically what you did on your first PC)
- Try the activation process and let them know it's the same PC, just with some hardware upgrades. I've had success reassigning an OEM key before using the telephone method.
- Buy a new (non-oem) license and register it with your account (I think you can have up to 5 licenses registered this way then you can pretty much arbitrarily revoke and reassign it among your future computers without hassle)
- Run the activator script
MS is generally pretty flexible regarding personal licenses and use. As long as you aren't trying to run the same license on multiple machines you should be fine. What you can't do is move the license from the OEM machine to your new custom build and expect the OEM machine to remain licensed.
One note about pulling it from WMI: if you got a free OS upgrade (i.e. from 8 to 10) you may have been issued a new key that's different from your original OEM key. This might cause some issues when talking with the agent.
Your luck with phone activation may be different with different agents too, so it might be worth calling back a bit later if you don't succeed at first.