Buy alternative from another company that has a less restrictive licensing scheme, make sure you are happy with the definitions in the EULA
If you want to go the legal route, see what they define “lifetime license” as in the software EULA. I am not a legal expert, so ensure you get professional guidance should you choose this
If you still have the original computer kicking around, depending on how the software licensing works they may have a license file saved somewhere (maybe in appdata, or program files). Grab that and pop it in the same location on the new system and see if that works