My computer is at the end of its life and I was looking to get a new computer. If I have a currently have a one month trial of Sketchup Pro on the old computer, will I be able to continue this trial version on a new computer?
Yes. You will be able to continue the trial on the new computer.
You should try to remember to sign out of SketchUp in the old computer, to make sure you have the spare sign in capacity on the new machine.