I'm not the sharpest knife in the drawer.

Just to make sure I'm understanding your situation:
1. The laptop originally had a total of 1GB RAM. Each slot contained a 512MB memory stick.
2. You replaced each of the 512M sticks with a 1GB stick for a total of 2GB RAM.
According to The owner's manual referenced in my post # 2, your computer should have one memory slot (called DIMM A) under the keyboard and a second memory slot (called DIMM B) located on the underside of the laptop. The instructions (starting on page 115) say in part:
NOTICE: If you need to install memory modules in two connectors, install a memory module in the connector labeled “DIMM A” before you install a module in the connector labeled “DIMM B.” Insert memory modules at a 45-degree angle to avoid damaging the connector.
If you followed these instructions it's possible that one of the memory modules didn't get seated properly and isn't making a good connection. Or it could be a defective module. So start from the beginning. Remove both of the 1GB modules. Insert one module in slot DIMM A
only. Reinstall the keyboard and turn on the computer. If this 1GB module is installed correctly and is not a defective module, your computer should recognize it and function normally. You can check this by clicking the Start button, then
right-clicking Computer, then clicking Properties. A new screen will open giving system info including how much memory is installed. It should show 1GB. If the module is not recognized by the computer it could be defective. Try the other 1GB module in slot DIMM A.
If the module in DIMM A is working properly go ahead and install the second module in DIMM B. Again, follow the instructions in the owner's manual. Hopefully you will have both modules (the full 2GB RAM) recognized. Or you will be able to isolate and tell if one of the modules is truly defective.