I'm thinking that is a bad omen. Although hard to tell without sitting before the computer, your symptoms are compatible with a failed "PAV" board. "PAV" stands for "power/analog/video" and they tend to get baked in the under-ventilated iMac G3 case. It has no fan, but should have. The PAV board is a common failue point for iMac G3s that have seen a lot of use.
That said, you can check a couple of things. If the computer has been off wall power for a long time the internal backup battery (or "PRAM" battery) is surely dead. This is the battery used:
NewerTech 3.6v Lithium 1/2 AA PRAM Computer Clock Battery
You access it through the RAM door on the bottom of the case. A dead PRAM battery is not alwasy a sure casue of what you see but it is worth trying.
While in the RAM compartment note there is a small button, a PMU reset button. The image in this link shows its appeaance and location:
https://farm3.staticflickr.com/2554/3832183809_3e903f2c20_z.jpg
Press it ONCE and for ONLY about a second. Any longer can create non-recoverable problems.
And, while the RAM door is open, remove and reseat the RAM just because it is easy at this point.
If you have the gray system disks that shipped with the computer, find Disk #1 and try booting from it. Hold the C key during boot and keep holding until you get a usable dektop or the computer appears stuck. Booting from a CD takes longer than normal so don't rush it too much.
If it boots from the CD/DVD then we need to talk more, so let us know what you find.