Here are the suggested specs for both games. Your motherboard is going to struggle with that Doom 2016 game. Looks like your motherboard also doesnt support the Phenom II x6, and your stuck with a maximum of a Phenom II x4. This could fall short of the requirements to play the game smoothly.
Looks like your going to need to build a new computer or if looking to cut corners in price of a new system, recycle the old computer guts into the new build. Reuse the case, RAM if it is in fact DDR3, and drives. Buy new 500 watt power supply, motherboard, CPU, GTX 670 or better video card, *Plus Microsoft wants you to buy a new copy of Windows because they pair up the licensing with the original Motherboard/CPU. So your "suppose" to buy a new license to use the OS that your old system has on it already.
What does your budget look like, maybe you can keep the old system alive without gutting it for parts and just build a new system or buy a new system?
Additionally if you want to test the game requirements you could buy the games and test them on what you have now. I have done this before and found out that games that call for a Quadcore 2.5Ghz CPU for example actually play ok on a Pentium E5400 2.7Ghz Dual-Core. My video card matched the game requirements but CPU fell short of the requirements, but the game played and played well on the Dual-Core. Only thing with the Dual-Core was that there was no multitasking when running Dragon Age Inquisition, it was play that game and no browser or anything else running to get it to run smooth on that Dual-Core. So If you want to test the waters with your older system you can since you will be buying games anyways, so buy the games and see. You can then install the GTX 670 or better video card and a 500 watt power supply if you dont already have one in it, and see if the Athlon II x4 will be enough or not. If its not enough then build a new system and take the GTX 670 or better card and your 500 watt power supply and use it for the new build. In a testing of how low can i go and play World of Warcraft for example, I set core affinity to 1-core for World of Warcraft on a Sempron 3850 quadcore at forced underclock to 700Mhz and integrated Radeon HD8280 graphics and the game ran and was playable, but the game runs far better when all 4 cores are available and clock is at full speed of 1.3Ghz. Your 2 games here would never run on my 25 watt electron sipper though.
Rise of the Tomb Raider
OS: Windows 7 64bit.
Processor: Intel Core i3-2100 or AMD equivalent.
Memory: 6 GB RAM.
Graphics: NVIDIA GTX 650 2GB or AMD HD7770 2GB.
DirectX: Version 11.
Storage: 25 GB available space.
DOOM 2016
Minimum Spec (720p)
Windows 7, Windows 8.1, Windows 10 (64-bit versions only)
Intel Core i5-2400 or better / AMD FX-8320 or better.
8 GB RAM.
NVIDIA GeForce GTX 670 (2GB) or better / AMD Radeon HD 7870 (2GB) or better.
Up to 22GB HDD space.
Steam account.
Broadband internet connection.
Note: Also found that about a year ago you also inquired about help on this same system and here is info from back then to help now as well:
http://www.computerhope.com/forum/index.php?topic=153377.0
