I've had to start a new profile several times because I got new computers. Coronation had traded me two Lolzies and a Myraid. Iceburg traded me a Sleaf and Cesleock. HOWEVER! I do have my old computer I will try to save up to by a thumb drive and I will transfer my profile to the new computer.
If you're unable to get a flash drive or similar device, maybe it's possible to find a method that lets you upload the necessary files to an external source that you can access with another computer?