Supposing Windows 10, I only know of two choices. The easy one might work, I've never tried booting into Safe Mode With Networking and running PSE in that state. If successful you could then sign out from the Help menu and your mission is accomplished.
The other option is to log into your Adobe account on your new machine and click on Support > Help Center. Note the Chat icon in the lower right portion of that screen where you can request an activation reset. Some have said that typing AGENT right from the start spares you the frustration of chatting with a chat bot and I'm inclined to believe them. Make it clear to whomever that you only need your activations reset or risk needlessly waiting an extended period for tech support. I'm not sure why registered users aren't permitted to do this themselves either. That'd be nice.