Diagnosing system failures and quirky behavior can be a crap shoot, as the same symptoms can point to any number of culprits. But unless you have reason to believe a specific component is at fault, most troubleshooting quests usually start with the RAM.
Testing for faulty memory is relatively easy to do thanks to a diagnostic tool called Memtest86 . This handy program runs a series of tests on your RAM, spitting out any errors when/if it finds them. And because Memtest86 runs before Windows has a chance to load, you won't be interrupted by further blue screens while it tests your memory. If you have a faulty kit of RAM, you may see hundreds of errors right away, or in less severe cases, you may need to run several passes (I recommend you let it run overnight).
To get started, you'll need either a blank floppy or CD/DVD disk, then download the latest version of Memtest86 (v3.3 at the time of this writing) for whichever media you plan to use. If using a floppy, double-click the install file, which will open a command prompt with step-by-step instructions. For CD or DVD installations, burn the ISO file as an image, and NOT as a data file. Most CD/DVD burning programs, such as Nero and Roxio, will do this automatically upon double-clicking the ISO, and other programs, like the free CDBurnerXP Pro will not, requiring you to specify you're burning from an image (click on File and select Write Disk from ISO File...).
Once you've made your Memtest86 diagnostic disk, the next step is to boot from it. Stick the disk in the appropriate drive (if you manage to get the floppy to work in an optical drive, or vice versa, I'd like to hear about it!), then restart your system. You may need to change the boot priority in your BIOS so that your system doesn't automatically boot from your hard drive. If so, hit the DEL key during the POST screen (some older systems may require you push F1, F2, ESC, or other combinations ). Once you've set the approriate boot priority, Memtest86 will load and run automatically.
If your RAM settings are correct, then test one stick of RAM at a time. While both sticks could be faulty, it's more likely that just one of them is defective. Also test the stick(s) in each DIMM slot to rule out the possibility of a faulty slot, while also providing you with an opportunity to verify you're using the correct slots for dual-channel operation.
Almost all RAM manufacturers offer lifetime warranties on their chips, so long as you didn't kill the modules by overclocking/volting. And if you inadvertently OC/d/OV'd, be upfront with the manufacturer (you're on the honor system with this one) - the companies worth giving your business to will be more apt to work with you in these situations.
If you do RMA a dual-channel kit, insist on returning both sticks, even if only one is defective. Why? Because dual-channel kits are supposed to be tested by the manufacturer to ensure they play nice together. The chips under the heatspreader on your replacement kit may differ from the ones on your existing kit, even if the make and model are the same, and it's when you mix and match chips that incompatibilities are most likely to occur in a dual-channel environment.