Why would 2 sticks of 2GB RAM not work together, but work individually in my Macbook?
This is down to a limitation in some memory controllers and how they handle memory sticks with different memory characteristics (also add into the fact that you have no control over these settings in EFI as you might have in a non-EFI BIOS)

When you put both new sticks in, the memory controller is trying to set up the memory according to the specs advised by the PNY SODIMMs, however it is having problems with that configuration and fails to initialise the memory.

When you put in a stick of the older RAM, it changes the configuration to use the slower RAM's settings and the second stick of RAM is actually running at the slower speeds and timings of the old RAM and these are invariably "slower" and more conservative than those the PNY sticks can run at.

The other posters are correct, the only solution is to get different RAM and try those. I would also advise to use a more reputable brand, the cost differences are minimal and the warranties are better.