Optiplex 980 1 3 4 error code Solid Blue Power Button

1-3-4/blue isn't a documented error code, but you probably already know that...

I'd suspect a RAM issue because 3,4 = memory failure, and 1 = no memory detected. You can try this:

1. Power off, unplug and press/hold power button for ~15 sec
2. Open case and carefully reseat RAM modules in their slots - you may need to remove the optical drive to reach the RAM modules
3. Used canned air to blow out all the dust bunnies
4. Remove motherboard battery and press/hold power button for ~30 sec
5. Reinstall battery (right-side-up)
6. Try to boot with only mouse, monitor and keyboard connected

If that doesn't help:

1. Repeat #1, above
2. Remove all modules except the one in slot 1
3. Repeat #4-6, above

Then swap all modules into slot 1 to  see if you can identify a bum module:

1. Repeat #1, above
2. Swap RAM modules into slot 1
3. Repeat #4-6