Did both memory modules come together in ONE kit, or were they purchased as separate sticks?
Truthfully, if both sticks work in both slots on the motherboard, but won't work together, there are only a couple of reasons why that might happen.
1. The memory is not compatible with each other. This can happen, and OFTEN does, even when they are the exact same model number but were not factory tested for compatibility with each other.
2. One or more bent pins on the CPU. The memory controller is in the CPU and we've seen many systems that would run with a single stick regardless of which slot or stick it is, but would not run with multiple sticks in a multiple channel configuration because there was a bent pin affecting the memory.
3. CPU cooler "cocked" in the socket, due to being tightened down more on one corner or side than the others. This can cause it to act like there is a bent pin because when the CPU gets cocked in the socket there is often a loss of contact with the pin bed by one or more pins.
Alternatively, you might FIRST want to install both DIMMs and then do a hard reset of the BIOS as follows, before investigating anything else. If however you know they did not come together in one kit, then I'd start by getting rid of that memory and getting a kit that consists of two factory tested, matched DIMMs.
BIOS Hard Reset procedure
Power off the unit, switch the PSU off and unplug the PSU cord from either the wall or the power supply.
Remove the motherboard CMOS battery for about three to five minutes. In some cases it may be necessary to remove the graphics card to access the CMOS battery.
During that five minutes while the CMOS battery is out of the motherboard, press the power button on the case, continuously, for 15-30 seconds, in order to deplete any residual charge that might be present in the CMOS circuit. After the five minutes is up, reinstall the CMOS battery making sure to insert it with the correct side up just as it came out.
If you had to remove the graphics card you can now reinstall it, but remember to reconnect your power cables if there were any attached to it as well as your display cable.
Now, plug the power supply cable back in, switch the PSU back on and power up the system. It should display the POST screen and the options to enter CMOS/BIOS setup. Enter the bios setup program and reconfigure the boot settings for either the Windows boot manager or for legacy systems, the drive your OS is installed on if necessary.
Save settings and exit. If the system will POST and boot then you can move forward from there including going back into the bios and configuring any other custom settings you may need to configure such as Memory XMP, A-XMP or D.O.C.P profile settings, custom fan profile settings or other specific settings you may have previously had configured that were wiped out by resetting the CMOS.
In some cases it may be necessary when you go into the BIOS after a reset, to load the Optimal default or Default values and then save settings, to actually get the hardware tables to reset in the boot manager.
It is probably also worth mentioning that for anything that might require an attempt to DO a hard reset in the first place, IF the problem is related to a lack of video signal, it is a GOOD IDEA to try a different type of display as many systems will not work properly for some reason with displayport configurations. It is worth trying HDMI if you are having no display or lack of visual ability to enter the BIOS, or no signal messages.
Trying a different monitor as well, if possible, is also a good idea if there is a lack of display. It happens.