[NAME] This Dell document tells what  the beep codes mean =A reference guide to the XPS Desktop Diagnostic Indicators Seven beeps is a CPU failure. Since a CPU failure is rare, I don't think you can rule out some sort of motherboard failure that makes it appear that the CPU has failed. Assuming you have an i7-3770 (the XPS 8500 specs 3rd gen I5 and i7 CPUs), I see prices on eBay from $40-$50 for a used CPU. I also see prices in about the same range for a used motherboard.
My 2011 Dell XPS 8300 won’t boot up. Running Windows 7. When the power button is pressed the fans come on and the power light turns orange, and it beeps.  I have changed the CMOS battery, removed each ram separately (12GB in total) and tried to boot but problem persists. I have disconnected the PCIe graphics and plugged in a VGA monitor but still nothing. Tried booting with HDD disconnected, DVD drive, etc. but no luck there either. Green power light on PSU is on and powering things ok. Can also hear the HDD (2TB) spinning up like normal but do not have another for diagnostics. What would you try next if you were dealing with this? Thanks! PS. Problem started on its own one day and not because I changed CMOS battery, Also no start up screen or BIOS coming on.
XPS 8300, won’t start, orange light, seven beeps