I have a dell dimension E510 and it currently will not boot up. The codes in the front panel I am receiving are 3&4. I research and found out this meant an issue with memory module. I removed and replaced memory module. The first time, the computer booted but then it shut down and error bodes 3 & 4 were displayed on the front panel. Please assist with having issued resolved. Thank you.

Try removing the memory module and clean the memory with a soft brush. Clean the slots on the motherboard and place the memory again. Make sure the memory is placed properly. (Both switchs on the memory slot should be holding the memory module in place)

If not working try placing memory in another memory slot on the motherboard.

If still not working, try swapping memory with a computer that has same type of memory.
Try the memory on another computer.
Try the memory of the other computer in the Dell Dimension. By doing this you'll determine waht causes the problem.

Test or Replace your PSU then test all leads that are attached to your hard drive sounds like a faulty lead of some sorts then
try replacing all the leads that attach to your hard drive including electrical extensions IDE,SATA and the ones that attach from your motherboard to hard drive
make sure all leads that are attached to your drives dvd\cd 3 1/2 inch floppy have secure connections and are not faulty or just replace them they are probably old and faulty because a computer has to have an end to the circuit any fulty leads will lead to no boot up
good luck