Removing the cover from the case: come on, people! Use force, but use it gently! There is no way to break things if you turn it into the direction of the second dot (to the left, counterclockwise). If you have to use force, don't push down towards the case, but use this force towards the intended cover rotation – you obviously have to push down also for the grip, but other than that: turn, baby, turn!

You should try to find out if the DIMM or the slot is broken: I suppose you tried to switch the DIMMs? The easiest way is to try only one DIMM (memory module), first in the lower slot, then in the upper slot.

IMPORTANT: reset the PRAM after altering the configuration, i.e. after moving a DIMM to another slot. (Hold Cmd+Opt+P+R when turning on the Mac and keep holding the keys until you've heared the start chime two times.)

https://support.apple.com/en-us/HT204063

If the one DIMM works in both slots, the slots are okay. Now try the other DIMM. If the second DIMM also works in both slots, I frankly have no other idea than to try a different version of OS X to rule out the possibility of a software problem.