Dell Optiplex GX620 computer beeps when powered on. The beep sequence is 1-3-2. What does it mean and how do I fix it?

SOURCE: optiplex gx620 black screen stuck on safe mode

Look at the motherboard (mobo). Failure of motherboards is usually due to breaking capacitors. A few years ago a capacitor company stole the "recipe" for making capacitors from another company and tried to make their own, unfortunately they did not get the ingredients right and the capacitors started breaking after 2-3 years of use. They sold these capacitors at very cheap prices and a lot of computer companies and power supply makers bought them. This is easy to diagnose. Look for capacitors (caps) (they look like little tiny soda cans) on your motherboard (mobo). They should be perfectly flat on top and not bulged or swelling or leaking anything.
You could also try to change out the power supply if you can find another one that fits it.

SOURCE: Dell E510 Memory

I deal with this sort of thing alot with servers. Easiest thing to try first is reseat the memory.

SOURCE: i have a dell optiplex gx620 and it wont turn on

As you can imagine, this is not simple thing to diagnose.
First, we need to try Dell's steps to fix...
Remove non-essential peripherals…
Except for the monitor, keyboard, and mouse, remove all external peripherals including:

• Scanner
• Printer
• Modem or Network cables
• Personal Digital Assistant (PDA)
• USB flash drive or other external Hard Drive
• Any other external devices (e.g., USB-attached devices)
• Remove the computer from the docking station, if you are using one

Remove non-essential peripherals…
Except for the monitor, keyboard, and mouse, remove all external peripherals including:

• Scanner
• Printer
• Modem or Network cables
• Personal Digital Assistant (PDA)
• USB flash drive or other external Hard Drive
• Any other external devices (e.g., USB-attached devices)
• Remove the computer from the docking station, if you are using one

Try rebooting. If that doesn’t work, Dell states you need to do the next step.
Remove and Reseat Basic Hardware items:

1. Power Cord
2. Memory
3. Hard Drive

At this point, Dells says if that fails contact them.

If my hunch is correct, you may have something on the motherboard shorting a connection or you have a blown capacitor. Get some “canned air” and blow out the computer thoroughly. Some people have reported the same symptom having dust or other debris causing the issue, so give it a good blowing out,

At the same time, inspect your motherboard thoroughly for an anomalies. If you see anything resembling the picture below, you have a serious motherboard problem which will require replacement.

SOURCE: Adding network drivers to dell optiplex gx620

Just download the drivers here the link http://support.dell.com/support/downloads/driverslist.aspx?c=us&l=en&s=gen&os=WW1&osl=en&catid=&impid&SystemID=PLX_PNT_P4_GX260

SOURCE: 4 long beeps a pause then a further 2 long beeps

check the following link to determine your problem

http://www.computerhope.com/beep.htm