My suggestion then is that there is now dust in a DIMM slot, which is preventing one or more contacts contacting properly. Clean it out as well as you can, and you'll probably be fine. You can try using one stick and/or moving one or both sticks around if you want.
DIMM slots were cleaned out, contacts on the memory sticks as well and still the exact same thing. Nothing on the screen and just the group of three beeps.