Screwing down the heatsink TOO tight, can cause the DRAM light to come on, or any number of other problems. So, when installing the CPU cooler you ONLY want it to be snug, fully seated, then maybe a VERY small additional 1/16 to 1/8 of a turn. You do not want to overtighten it OR tighten it more or less in one spot than in all others. That's why I recommend for high pressure mounting heatsinks that you alternate corner to corner or side to side in turns of no more than 1.5 turns until snug, then lightly tighten it down just a little more. No more than a quarter turn at MOST.
This isn't USUALLY the cause of problems like this, but it happens frequently enough to be worth being aware of.
About the only way the CPU would cause the DRAM light to come on is if it is faulty (Pretty rare. Like, in 30 years I've seen two or three ACTUALLY faulty CPUs that came from the factory that way.) but usually any CPU that fails is due to some kind of user error like a bent pin from improper installation, being dropped on the floor which damages something inside it or bends some pins, incorrectly overclocking with too much frequency or voltage, long term overclocking or a short somewhere that zaps something. Or if the CPU cooler is cocked from an uneven installation pressure, which can cause it to cock in the socket and break the connection between some of the pins and the contacts inside the socket or for Intel, the contacts with the pins on the motherboard.
So yes, the CPU can definitely cause the DRAM light to come on because the memory controller is IN the CPU, but it would be pretty rare for it to simply be a faulty CPU unless one of those conditions above was met, or you bought it used and don't really know the history of abuse it may have gone though, or you are that one in probably several thousand that actually comes with some kind of factory defect that results in either an instant failure or a failure within a relatively short amount of time.
Far more common would be, well, ANYTHING else. That doesn't mean it CAN'T be a CPU, because I've seen a handful of them fail here in the forums over the last five years, but I personally have only seen three myself that I know for a fact were factory defect failures.
My recommendation would be to follow the guidelines in my bench testing guide. That's really about the best way to figure out what's going on and the fact is that in some cases you just can't figure it out without throwing a few parts at it, since most of us lack the specialized equipment required to actually test CPUs and motherboards. Even most repair shops don't have that kind of equipment, and much of what they do is accomplished by basic troubleshooting and swapping out parts until the problem is found.
Finding the problem through bench testing If you are here then it’s likely you have encountered a serious hardware issue and have been unable to resolve it using the standard no-POST troubleshooting procedures. If you have not yet attempted to resolve your issues using the no-POST...
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