There is no picture on my screen when booting up my dell optiplex gx620 there is 2 buzzing noise when turned on

You've got your speaker wires on the wrong pins on the MB.

Motherboards use signals a radio signals to communicate across them. Some on board soundcards pick these signals up. Try purchasing a better sound card. This might eliminate some of those on board noises you are hearing. Hope this helps.

If you tried to install a BIOS up-grade and it failed, then your motherboard is toast.

this logo with the dell picture can be disabled from the Bios settings ..to get there press F2 on start ..or what ever key is indicated on that logo screen for to go in set-up ..and in there under advanced settings look for screen logo ..and disable it ..after that f10 to save settings ..or in some bios editions it will ask if you want to save changes on exit ..select save changes and exit ..
just look carefully in the tabs ..cause this option is there for sure..and disabling the logo will kinda make it boot faster ..

I have the same problem. I think it might be that the computer is not powering on all the way do to overheating. Try replaceing the CPU fan.

The first thing to check would be the CMOS to see if there is a setting for "case intrusion" or something to that effect. Some computers have sensor that goes off the computer's side panel is opened. I believe this can be disabled in the CMOS and/or it's just a wire connected to the motherboard that can be disconnected.

It could also be an important fan, like the CPU fan, isn't spinning fast enough which may or may not lead to an over-heated CPU.

Also check to be sure all the memory sticks are firmly seated.

If it doesn't look like any of those it could always the the power supply. See if you can borrow one for a little while for testing purposes just to see if it works.

If none of those pan out I would say call Dell support and see what they say.

if the system doesn't boot past the Dell Screen, the most likely issue is the hard drive.
See if you can bring up the F12 menu at boot and run HDD diags.
If you can't do that and have the dell resource cd, you can try booting to that CD, and run diags there

You may have a problem with your power supply(the loud fan noise) and eventually it may get too hot and will cause problems like not fully booting.

try going to the bios by pressing f2 or delete key on the keyboard at the dell logo.
if you are able to enter the system setup screen, reset the bios.
to reset the bios, press num lock, caps lock and scroll lock so that all 3 lights on the keyboard are on.
press alt + e and alt + f keys.
press esc twice
then select save changes and exit.

also try booting through the safe mode by hiiting f8 on the dell logo.

you can also try booting through the dell resource cd or win xp cd.

Your cd Rom is also not working properly