Are you sure that the RAM modules are compatible with the motherboard of your computer? Have you stuck to the process for adding RAM modules described in the manual of your computer model?
Apart from what is told in the manual, you must unplug any AGP graphic card you have in the computer before adding the new modules. The reason is the connection between the graphic card and the RAM, it has some RAM MB "reserved".
If you have done all of the thing said, run memtest from Grub or download memtest86+ and run it from a CD at boot if you cannot find the Grub option.
I have edited the answer to note these paragraphs of the manual I had found by searching Dell Dimension 8200 (Please, ensure it is the right one and read it carefully):
NOTICE: If you remove your original memory modules from the computer
during a memory upgrade, keep them separate from any new modules that
you may have, even if the new modules were purchased from Dell. Your
original memory modules must be installed as a pair in either
connectors RIMM1 and RIMM 2 or RIMM 3 and RIMM4. Do not pair one
original memory module with one new memory module in connectors RIMM1
and RIMM2 or RIMM3 and RIMM4. Otherwise, your computer may not start
The only two valid memory configurations are:
* A pair of matched memory modules installed in connectors RIMM1 and RIMM2 with continuity modules installed in connectors RIMM3 and RIMM4
* A pair of matched memory modules installed in connectors RIMM1 and RIMM2 and another matched pair installed in connectors RIMM3 and RIMM4
I am not an expert, but the motherboard does not seem to allow to add RAM memory unless you ensure that you get matched RAM modules. They must be a pair RAM modules made to work together and originally sold together too.
And if you are using only two RAM memory modules, you should plug the connectors modules into the right connectors before plugging the memory modules in:
NOTICE: Be sure to install memory modules in the first two memory
connectors (RIMM1 and RIMM2) nearest the processor before installing
memory modules in the outer two memory connectors (RIMM3 and RIMM4).
Another option is to buy two pairs of matched RAM memory modules of the same capacity:
NOTICE: If you upgrade the memory, the memory modules must be upgraded
in matched pairs of identical MB capacity in both memory connectors
RIMM1 and RIMM2 or memory connectors RIMM3 and RIMM4.
Adding RAM modules to other motherboards with four connectors seems lees requiring. I think you can sometimes plug two RAM modules of the same capacity but bought separately into RIMM1 and RIMM3 or RIMM2 and RIMM4 and the computer works.
PS: I am sorry for my rough English.