Apologies for reviving an almost 10 year old topic, but just this week I got the same Compaq Deskpro 2000 5133 and had exactly the same problems: Machine didn't boot reliably if at all (mostly not).
No video signal, no beep, just fan and green power LED. The machine came with a dead CMOS battery and the 2.5GB hdd (win98) didn't have the diagnostics partition.

What worked for me was the following:
1) Install an external CMOS battery using 3x AA batteries (connect pin #1 to + and #4 to -)
2) Install the diagnostics partition using sp4711.exe

With the battery and diagnostics partition in place, the video signal now comes on immediately every time and the machine boots reliably - no more errors, no more hangs.

Unfortunately that solution occurred to me only after I had tried every combination of memory, onboard/off-board video cards, riser, hdd, cdrom, fdd - and had already given up and ordered a replacement board with cpu on ebay 😉.