I would not expect Intel's stress test to use all available RAM in your system. That's not quite the point of the test. It's more of a general pass / fail system for the RAM subsystem, at it's current settings, under a heavy work-load, rather than a complete bit testing system, to verify every memory location as being good.
If Windows Memory Diagnostic is reporting an error with your RAM, you would do well to get a second opinion and dig further.
There are plenty of programs out there, but here are links to two respectable ones, both of which are free, and I would recommend one or even both, as one is a fork of the other and in rare occasions will have differing opinions about the reliability of RAM.
MemTest86:
http://www.memtest86.com/
MemTest86+:
http://www.memtest.org/
If either of those also return memory errors, your best bet is to consider at least some of your RAM as defective or malfunctioning.
Even while not defective, your RAM can easily return bad values if it's improperly configured, so a result of errors being returned is not yet all you should do to determine a defect.
If you are comfortable, you should really start by determining that your RAM is configured properly, even before trying to do any tests upon it.
With a free program such as CPU-Z:
http://www.cpuid.com/softwares/cpu-z.html
You can look at the SPD (Serial Presence Detect) information for each of your installed memory cards and with that information written down, you can look at the actual running speeds of the memory. If the column that matches the speed your RAM is running at, has values that differ from your actual running values, you need to correct those timings through BIOS.
Be careful though, as messing with things like that can render your computer unbootable. If you're really uncomfortable with this, I recommend having a more experienced friend or even a shop do further work.
If you have determined all of your memory settings are within the designed specifications for the modules, or have adjusted them to be within the rated tolerances, then you can finally get to testing the RAM and expect reasonably realistic results from a memory testing program.
Once you have determined that you are getting memory errors, assuming you can't read memory addresses to know which module inside the computer it is, you need to start isolating your RAM modules inside the computer, then retesting. You will likely find it's only a single stick out of 2 or 4 that is malfunctioning, unless you have bad settings. Pulling all but one module, then retesting, will tell you which module is defective.
Once the defective memory module has been determined, you will want to contact the manufacturer to request an RMA (Return Material Authorization.) Most reputable brands of RAM module manufacturers have a lifetime warranty and are fairly easy to work with.
If you have multiple modules of the same RAM installed, you will want to send the RAM modules back as a pair. With something like a Post-it note, mark the defective module, then package up the pair as per the RMA requirements. The reason for this is, RAM has very small tolerances, and the faster the RAM, the tighter the tolerances. To run two sticks or more together, they need to be as close as possible, so most factories take modules from the same batch and pair them together in groups of 2 or 4. They will make sure you get a closely matched pair back from your RMA, if you send a matched pair.
Anyhow, hope this helps some.