Hi,
If I remember correctly, these HP Vectra-s had a BIOS specific to Vectra models instead of using one of the common ones like AWARD or Phoenix BIOS. IIRC 4 short beeps unfortunately means "generic error during initialization" and would be followed by printing a 4 hex-digit code to the display, but unfortunately in your case it seems that the display didn't initialized properly or haven't yet got to display initialization.
In the "Diagnostics done" list you already checked the usual suspects that I would check at first, the only thing I can suggest at this point is to try it with a known working video card, may be it will be able to output the 4 digit diagnostic code.
Also while I'm not sure about this specific model some older HP Vectra-s needed a boot floppy to be able to setup the BIOS, you might wish to make one before proceeding if you get to the point that it is able to boot.
Sorry for being unable to give more concrete advice, hopefully someone who has more direct experience with this exact HP Vectra model will come along and able to give more specific help.
"A process cannot be understood by stopping it. Understanding must move with the flow of the process, must join it and flow with it." - Dune