eMac freezes randomly, open window turns into broken up jibber

Have you tried running the Apple Hardware Test?

What messages, if any, do you get when you boot from your OS X Install Disk and opne Disk Utility from the Installer menu to run Repair Disk on the hard drive? (Refer to Using Disk Utility and fsck)

How old is the eMac? Is it still within the one-year hardware warrenty, or did you purchase the three-year appleCare extended warrenty?

Is the Hardware Test disc the one that came with the eMac? (On Mac models that came with OS X Install on a Restore DVD, AHT is a separate partition on the DVD, which can be booted using the option key to bring up Startup Manager).

The video "card" in the eMac is actually a chipset on the logic board, so bad video hardware does involve replacing the logic board.

This doesn't help. but my first thought on seeing your picture was 'addressing bit failure in the video memory'. Unfortunately, as you already know, the video 'card' on the eMac is a chipset mounted to the logic board, and the only repair I'm aware of is replacement. An Apple Service Provider could give you an estimate but unless your eMac is still within the standard one-year hardware warrenty or you purchased the three-year ApplceCare extended warrenty, that's not an attractice cost-benefit tradeoff.

On the chance that I'm wrong and it's some unusual system corruption, look again for the Hardware Test disc. It can be tricky figuring out where it is; on early eMacs it was always a separate CD, on recent eMacs it's a partition on the Restore DVD, and on models in between, it depends on whether the OS X Install disc was on a DVD or not. You might try booting from your OS X Install or Restore disc using Startup Manager to see if Hardware Test is on a partition.

If nothing else, booting off the OS X Install disk (as if you were going to run Disk Utility > Repair Disk to check the drive) should further confirm if the problem is in the video hardware rather than in the hard drive's OS: if the broken display appears when booted from the OS X Install disc, it's pretty certainly the video hardware.

The EXACT SAME THING was happening to my emac.
http://users.vianet.ca/dtrudel/crashA.jpg
http://users.vianet.ca/dtrudel/crashB.jpg
http://users.vianet.ca/dtrudel/crashc.jpg
When it happened, I couldn't force quit, had to reboot. Check your system logs, I'll bet you have something saying something like:
"ATIRadeon::submit_buffer: Overflowed block waiting for FIFO space. Have 5, need 6."
I've tried all the standard troubleshooting stuff, repaired permissions, ran Onyx, used the TechTool Deluxe, Apple Hardware Test, ran tests on the RAM, Video Ram, removed RAM, re-inserted RAM, etc, etc...all of which says everything is fine....I also created a new user, and even reformatted, but problem still occured, and gradually got worse and worse over the period of a few weeks.
I took it to a service center under warranty. I'm still waiting to hear back from them, and to find out what they say the problem was. I'll post an update when I get it back.

The 1.25GHz eMac's RAM specs at Crucial say:
DDR PC2700 • CL=2.5 • UNBUFFERED • NON-ECC • DDR333 • 2.5V part number CT368142

The iMac specs depend on whether you have an early or late model; e.g., the G4 (800Mhz) specs, also according to Crucial, says:
SDRAM, PC133 • CL=3 • Non-parity • 133MHz • 3.3V
(which doesn't match your eMac), but the later 1.25GHz iMac G4's specs are:
DDR PC2700 • CL=2.5 • UNBUFFERED • NON-ECC • DDR333 • 2.5V part number CT327964, which certainly looks like a match to me.

While the part numbers differ, I believe that's due to Crucial's bookkeeping. If you have the later iMac G4, you should be able to swap the RAM.

I have the exact same thing. I spent all day yesterday trying everything to fix it. It pretty much immediately crashes when I turn it on now either by freezing up or the jittery split up. Please help!!!!

Me again
Could this be a virus- why do we all have this at the same time? I went to look this topic up and it was the first one on the page- what are the chances that my problem is the number 1 topic. If its not a virus- is it not a problem that apple should take care of since we all have the exact same thing. My computer is only 1 1/2 years old. It should be perfect.

If it makes you feel any better I have the exact same problem that I took to CompUSA where I bought it to be fixed. Emac is 1-1/2 years old. Beleif is that it is a video chip or logic board problem.

It would appear that you have a hardware problem, probably with the video subsystem. As this is on the motherboard on an eMac, you'll almost certainly need a motherboard swap.