Memtest86 shows errors although modules aren't faulty, motherboard issue?

[GreatAvenger]

A while ago my PC started freezing under load, when playing games or running benchmarks. I ran Memtest86 a few times since and it reported a lot of errors every time, even when switching my two modules between four different slots. I've tested those modules in a different PC and they appear not to be faulty. The freezing persisted even when I installed two modules from my other PC, which are also proven to be working. I concluded that origin of problem is the motherboard. Interestingly enough, PC works fine when layed horizontally. I tried reverting it to vertical position, but it wouldn't even boot as the motherboard would beep three times. According to this guide, it means there is a RAM issue. http://www.computerhope.com/beep.htm Could it be a faulty motherboard?

RAM: Corsair Vengeance LP 8GB (2 x 4GB)
Motherboard: Gigabyte GA-970A-UD3 rev. 1.2

 

[ebm9000]

Faulty connections between the RAM slots and the motherboard. Horizontal only indicates that the slots are being weighed down by gravity just enough to make contact. The motherboard is probably faulty.
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The reason for Memtest to only show errors on the faulty PC is that enough pins on the ram stick make contact to tell the computer how much RAM there should be.