Dell computers are really fussy about memory and that sounds like an off brand--return it. see the reviews for that brand of memory--mostly bad. Check Crucial to see what might be a better fit. Most of us use crucial ram for Dell computers. BTW, 4gb of memory in the old computer is plenty especially if you have 32 bits version of windows.Save your money for a new computer.
I know this is an old thread but I have a similar problem with my Dell XPS 630I. I recently bought GEIL DDR2 dual channel 8 Gb 800MHz Ram. I run WIN 10 pro, 64 bit. Bios version 1.0.13. When I insert all the memory in the 4 slots windows starts normal (no strange beeps) and when I watch someting like ie on youtube, after a while I got a BSOD: IRQL NOT LESS OR EQUAL and sometimes: KMODE EXCEPTION NOT HANDLED. At that time I was running bios version 1.0.5. I reverted back to the original 3 GB of memory (2x 1GB + 2x 512 GB). Now I have upgraded my bios to version 1.0.13 and installed the 8Gb again. Now I get BSOD: SYSTEM SERVICE EXEPTION (KS.SYS). I removed 4 GB of the 8 GB and now everthing seems to work fine. I should have googled before I tried to upgrade my PC but it looks like I am not the only one who thinks this workstation should be upgradeable to 8GB. Does anyone have a solution? Is this problem motherboard related? Or is it Driver related?
FYI, here are all the BSOD's I have seen and it all started when I install the 8Gig:
-Driver IRQL not less or equal
-IRQL not less or equal (HDClass.sys)
-Kmode Exception Not Handled
-Page Fault In Nonpaged Area
-Critical Process Died
-System Service Exception (ks.sys)