Can I reinstall my Unity Pro License after it's been maxed out if my computer/hardrive fails?

I'm considering buying a Pro License and recently my laptop, which is my secondary system, died. Like, completely! I still don't know what happened exactly, but it's fried beyond repair. Fortunately my warranty will cover a new one, BUT, it got me thinking.. "What if I had installed Unity Pro on this? Would I be screwed? Or could/would the Unity folks work with me to reinstall on my new computer once it comes in?"

So again, to clarify, this is a hypothetical situation where I have 1 Pro License, and I've maxed my limit of 2 installations. Then one system is lost (fried, dead, destroyed), what happens then?