Having chips on only one side is optional. This is often done by MFRs to save costs on production.
As the others have said, 3 long and 2 short is HP's beep code for RAM fault detected. Since you said you've tried both RAM sticks in both slots (assuming you've been sensible in trying all 4 combinations to rule out both the RAM and the slots), the next thing you can try doing is buying new RAM sticks to put in.
Assuming that you've got an older laptop with DDR3 RAM, you can get a replacement 4GB RAM kit for £15-20 and 8GB for £30-35, so it's fairly cheap. Just make sure that the replacement you get has the same specs as your existing RAM (e.g. speed, voltage).
