Since the iMac G4 20" computer shipped with a 1.25GHz logic board and nothing less,
the actual replacement would have to be the same for it to function. A 1.0GHz board
probably would create more problems than it could solve; and video support, power
supply output & other details would likely not match the original demands of hardware.
(If the computer you have, originally shipped with a 1.0GHz processor on its board, the
model did not have a 20" LCD display; so that may be part of the issue, if you have
one part and it does not really belong with the others. Those do not interchange.)
And a 1.0GHz board likely requires a older, different kind of RAM than a 1.25GHz
needs to have, to run. This is why the question(s) and answer(s) are detailed. If you
have a download copy of MacTracker for use in a computer offline, you can look up
the general specs and some upgrade info, plus OS version information, within it. See
the site and
http://mactracker.ca to get a version of this for the sake of comparison.
Also, the web site
http://everymac.com/ has info and lists of resources, that may help.
+{These forum pages are generally supported by Apple, but the replies and content to+
+the user questions are the results of persons with varying amounts of experience, or+
+knowledge, or skills, or time on their hands and a fair grasp of using a search engine;+
+or, maybe some are actual technicians and persons who have training in their day job,+
+they stop by on occasion to help out. Regular Mac users, none receive compensation.}+
Hopefully the issue in your computer can be resolved without much additional expense.
Good luck & happy computing! 🙂