Try unplugging the battery and turning it on with the battery removed. In some situations, the battery itself will prevent the computer from powering on. If that doesn’t work, try reseating the RAM module(s). If there is more than one, try starting it with each one individually. There are numerous things that can cause this type of issue, it’s just a matter of running through each of them to find the culprit.
There are a lot of different things that can cause this type of issue. In order to give more guidance, we may need more information. Such as: Windows version (7, 8, 10) Current Build version (1709, 1803, etc...) Computer make and model The most recent causes of these issues, from what I've been experiencing, is the Windows 10 1803 update. This has been affecting both manufactured and custom built computers (desktops and laptops) with 5th generation and prior Intel processors or AMD APUs. The manufacturer may have released new drivers for the computer to fix the issues, but it may be necessary to revert back to a previous build version.
Unfortunately, you are only able to run AM3 processors on certain AM2/AM2+ motherboards, and only if the manufacturer provided a BIOS update supporting it. On the ones that are capable, you still won't have the full capabilities, as the socket/chipset weren't designed for it (such as Hyper Transport). Your best bet would be to find an AM3 motherboard, rather than gamble with your current one.
If the motherboard was designed in such a way, it would require at least one slot from each bank to be loaded. Laptop motherboards aren't standardized like most desktops, and that allows for OEMs to take creative liberty in their designs. If that one 2GB card was defective, it would still fail to post with the other cards in. Again, it may just be a flawed design. The maximum memory supported by your laptop's motherboard is 8GB DDR3 @ 1333Mhz, as per ASUS technical specifications. 32GB of RAM is not possible on this machine.
The processor can not be changed out. If you're looking for more speed, I would suggest installing more RAM and a solid state drive. As far as technical limitations are concerned, the motherboard can handle up to 16GB of 1333Mhz DDR3 SODIMM, running at 1.35v. The brand doesn't really matter, as they all do the same thing. Any 2.5" solid state drive will fit, and the prices have come down considerably. There are a lot of 480GB drives available around $130 +/- on Amazon. You'd notice a huge difference with just the solid state drive.
There is no realistic way to repair a processor itself. The only viable solution is to replace it. You should be able to find used Phenom x2/3/4s fairly cheap online. Update (01/17/2017): Also, most AMD FX series processors do not include integrated video capabilities. These CPUs were designed for gaming systems with dedicated graphics cards. There is a possibility there is, in fact, nothing wrong with the processor.