Do you have setup files? If so then just reinstall on the new machine. I dont know what the actual rules are but if you bought CS3 then IMO its yours to install on your computers for the rest of your life.

I have CS5 installed on my desktop and laptop. With my laptop i originally had it installed on WinXP but after i upgraded the OS to Win7 i installed it again. So technically i have installed it 3 times even though an individual is typically granted 2 machine activations.