Both of those LED codes point toward a system board failure. You can try replacing the CMOS battery as that system is approaching 10 years old and the battery may be weak. As per the service manual that battery is a CR2032. If that does not help then a system board has probably failed. And with a machine of that age an upgrade to a new far more powerful system may be the better choice.
So I have a Optiplex 990 and one day windows asked for a update and all went as usual until restart then the PC wouldn't POST and can't enter BIOS. I suppose it was a coincidence that it happened then. When I let the PC load without touching anything it starts loading and it gets stuck at the end and 1,2 led lights are lit. If I try entering bios or one time boot menu I just get a black screen with a blinking white line but the 1,3,4 lights are lit. I tried resetting the BIOS by removing the motherboard battery for 1-5 min, removed the GPU and tried on integrated graphics tried unplugging the RAM sticks one by one and removing the SSD and HDD. Nothing worked so far. And all of the hardware worked ok until now. I have changed some setting like what CPU core are used virtualization and Intel Turbo Boost but nothing too serious.
PC won't POST and can't enter BIOS