You cannot ignore the beep.
okay lets ignore the beep then.
With your system not working, the system (or case) speaker is your most valuable troubleshooting aid. Right now, you have three decision points that affect the path you need to take for troubleshooting:
1. Silence or beeps.
2. Different beeps.
3. Single short beep (good) but still no display.
If you cannot hear the beeps or absence of beeps, you have no idea what is going on and the proper troubleshooting path to take.
You need to install a system speaker. Otherwise you are limited to blindly changing parts. If you have a second computer with all compatible parts, that would be a plan, excessively suboptimal, yes, but a plan.