It could depending on what all is included in the testing feature, and what parts of the testing features you used...however, that's really one for some tech with more knowledge of that particular function than I have.
If I knew exactly what functions those tests performed, I could answer but exactly what is meant by hard drive, system and memory testing is unclear as to the general testing.
There are however, subsets to each of those tests that you can perform so...see what I mean? For example, there is a custom test for you to use for particular symptoms you are having. Perhaps you should go back and have another look at the testing features available before you go on, just to make certain you have crossed all the T's & dotted...as the saying goes.
You can read through the Dell Diagnostic usage instructions Here
. Long and short of it is, until you can get that thing to boot from a CD, there seems to be nothing more we can do here.
There are other means by which you COULD create your own bootable CD to bring a non booting system back to life, and if there is no one else you know who is willing to lend an install CD just for testing purposes, then you could investigate these other possible means...but before I suggest it here, I would have to consult with the Admin folks here because there may be some legal ramifications regarding the distribution of non licensed software. I doubt we will go that route so, look hard for some friend who can lend a hand first.
Certainly, if this were virus related and it was determined that you would need to reformat and reinstall that operating system, you would need a cooperative hard drive...but, you have said, you cannot even get the BIOS to recognize your optical drive when a boot up is performed while the CD is installed.
You could try some other installation CD if you can find someone else who has one simply because, it is also possible that the CD you used is damaged.
There is still the possibility that the motherboard battery could have dried up as PCB stated. Have you checked it? Do you recall, was the system keeping the correct date and time or was it constantly changing to something else after you made a correction to it?