Welcome to the joys of upgrading a closed system. Nope, you can't use the iMac's monitor as a second display.
There once was - or still is - an American company that would upgrade the CPU of the iMac G4 to a faster model; you had to send them your computer and they'd return it with a modified logic board. It was not cheap, but they'd upgrade the 1.25 GHz model to an almost 2 GHz version (or whatever the fastest G4 CPU was). I don't recall the name of the guys. Maybe somebody else here does. If not, try googling for "iMac G4 CPU upgrade" or something like that.
The coolest thing would be if there was somebody who'd put the main board of an Intel Mac Mini into the old iMac G4... *sigh* My girl friend still has a 17" iMac G4 1 GHz; would be cool to bring that machine into this millennium. After all, this was the most beautiful computer Apple -ever- sold.
UPDATE: Okay, the name of the company is DAYSTAR. Here's a review:
http://www.barefeats.com/imup.html
And this leads to their website:
http://daystartechnology.com/Apple_...h_Products/Mac_CPU_G4_Upgrade_iMac_FP_PS.html