Computer only boots with 1 stick of RAM.

Today I decided to fix my CPU heatsink (it was slightly crooked, not the left to right crooked, the up and down crooked, it didn't have any influence on my CPU's temperature but it bothered me). While unscrewing the heatsink, one of the screws that was connected to a washer came off from the motherboard (the treads were worn down and no longer fit into the motherboard), I quickly fixed it and decided to not mess with the heatsink anymore. As I powered on my computer, all of the system fans turned on, graphics card started spinning up, the HDD started to boot up but then after a few seconds, my computer turned off. After about 3 seconds, it booted back up only to turn off again after 4 seconds. Nothing appears on my monitor. The single beep that my motherboard usually emits doesn't happen. Then it just repeats until I switch off the power supply in the back. At first I thought I messed up the CPU itself but after researching online and testing my components, I found that my computer will only boot up completely if I have 1 stick of RAM in. I tested both sticks individually and they worked (they are 8GB Kingston DDR3 1600 mhz). I also tried different combinations of the RAM slots. I checked if any pins were bent and none were. I also have my old 8GB Ripjaws DDR3 1333 mhz that I tested and it is the same thing. Only boots with one stick of RAM. Is this a problem with my motherboard?

My specs are
i5 2500k @ 3.3 Ghz
8 GB Kingston DDR3 1600 Mhz (as of right now, only 4 GB)
MSI GTX 670 @ stock clocks
MSI P67A-C43 (MS-7673) Mobo
Seasonic 620W 80 Plus Bronze
Cooler Master Hyper 212 Plus Heatsink
Seagate 7200 RPM 750GB HDD

I also would like to say that my system was working flawlessly before I decided to fix the crookedness of my CPU heatsink. Funny thing was I was thinking in my head, "If it doesn't affect my CPUs temps, then why do this? I'm just going to mess something up and totally regret this." Well, it turns out I was right and should have just left the heatsink alone.