Is the iMac G3's display dead or something?
My impression is that the switch from ADC to DVI/VGA happened during the MDD era, so you have to be more specific about what hardware you had.
However, if you have an LCD that takes a DVI input, you CANNOT use the DVI to VGA adapter to plug it into a computer that outputs VGA. It doesn't work that way. It's meant for the opposite situation (DVI computer and VGA display); the difference is that LCDs that take DVI inputs typically do not accept analog signals over them. DVI cables can transmit both analog and digital, and video cards generally output both on the DVI port, so that is why you can use the cable when you have a DVI computer, but not when you have a DVI display.
If the system is DVI, then the port on the PM should look like this one:
If it is ADC, it should look like this one:
Note the features on the right side of the DVI port that look different.
Anyway, though, I think you're out of luck. If you have ADC, it will cost you hundreds of dollars for an adapter that will get the VGA output displaying on it. If you have DVI, I still think you're not going to find a cheap solution.
I would find someone's VGA monitor sitting around and borrow it. Plenty of LCDs floating around that support VGA.