Sounds like you have two chips and one of them is intermittently having r/w failures..
Agreed. It's most likely a bad or improperly seated stick of RAM, but itcould be a fault on the motherboard as well.
Here's the official word on that error from Dell's support site:
Probable Causes: Faulty or improperly seated DIMMs or defective system board.
DMR
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I believe the stock version of the Optiplex GX150 used the shared memory scheme in which a portion of main system RAM was dynamically allocated to video/graphics functions. If that's true, the fact that your getting a distorted video display as well as the general memory error message would indicate that your stick of RAM is "going south".
Since you don't have another stick of RAM to swap in, you should run an intensive memory-testing program such as memtest86.
Also- you said:
I get the "Dell" screen for a few seconds and then two beeps
Those beeps are system codes which could tell us a bit more about the exact problem; can you give a more specific description of the beeps (for example, are they: 2 beeps of equal duration or 1 long and 1 short or 1 short and 1 long, etc.).
DMR
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