You can only register your software once... usually done the first time you ever install it if you do it at all. Registration is not the same as activation. Activation is done every time you install the software.... the process where you enter your serial number to get out of a trial mode or otherwise fully enable the software after a trial period has finished.
You might end up with an issue if you try to work with a new ID if the software is already registered for another ID. You will not be able to support from Adobe as they no longer support CS3 and will send you to the forums to forage for help.
Thank you Ned Murphy, I had myself confused about registration and activation. I only use these apps fairly infrequently - hence why I have not come back again until now. The apps are on the new machine, and seem to be operating normally, though I haven't done anything to activate them in the new machine. However, I notice when I open them that I have an earlier version than I ended up with on the old machine. For example Photoshop ended at 10.0.01 on old machine - is now 10.0.0 on new machine - I'm presuming that is the version on the installation discs. Also when opening the apps I get an error message about the Adobe updater having crashed, and it won't re-start. So my question is now two-part - a) do I need to update beyond the original disc versions, and if so b) how do I activate, or how do I access more up-to-date versions, without having to pay for a complete new suite which I can't afford.
Thank you for your help