Could be either but eMacs historically don't have a trend to failing RAM slots found is some other models like certain G4 PowerBooks.
First thing is to remove and reseat the RAM. This makes sure nothing is loose and helps freshen up the contacts as the module slids out and back in. Do this and test.
Have you recently added RAM or other hardware, or did the three-chime signal start randomly?
If you've added RAM, take out what you added and test with the RAM loadout that you had before adding RAM.
In case you bought incompatible RAM, we need to narrow down which eMac variant you have. If you have access to another computer, please see this Apple article:
and post what you find for the variant. Note the article has you look at the LAST THREE LETTERS of the serai numbers to make this work.
If the problem turns out to be bad RAM slots, it's unlikely to be something you can fix. The usual repair is a new logic board that may cost as much as a refurb Mac Mini
If the chart shows yours is an "eMac (USB 2.0)" we need to do further checking. A significant number of that model had bad logic boards, although ti wasn't the RAM slots that were bad.
To get the question out of the way, can you confirm this computer once worked properly for you? Helps to establish a little history in these cases.
Next thing to try is one RAM module at a time. That can reveal bad modules and bad slots.
So the RAM currently installed was there when you got the computer?
The eMac (ATI Graphics) did not have any huge issues that affected a large number of computers the way the logic board issue did with the eMAc (USB 2.0).
Do any of the RAM modules have identifying stickers with a description, or a least a make and part number? If they do, post the info and I can see if they meet the specs for that model computer.
Older Macs can be very sensitive to getting the right RAM. RAM like EDO, buffered, registers and hi-density often made for peecees often fail in a PPC Mac. That eMac model has a max RAM capacity of 1GB (2 x 512MB modules).
My two trusted Mac RAM vendors are a long way from your door, but I'll post them so you can see the specs for proper RAM for your model:
Did you find any labels on the RAM sticks you have now?