Did you try each ram module individually in slot 1 to make sure that they're all working OK, you didn't say?
If they all work individually then try 2 modules in slots 1 & 3.
If that works OK then try 3 modules in slots 1, 3 & 2.
just trying to isolate if it is just a ram module issue, a particular slot issue or a ram controller issue.
Remember to disconnect the power from the desktop before removing /replacing the modules.
So slots 1 & 2 don't work at all and 3 & 4 do, is this correct?
If so then it seems like the controller for the 1st two slots or where they connect to the chipset has a problem
What is the board number of the motherboard? (printed on the motherboard itself)
The ram connects to the CPU via the chipset so if some slots aren't working, you may have to find the schematics for the board to find out why the ram controller(or the chipset) is not working properly.
Given that you have had other problems with the motherboard try doing a power refresh first, just to eliminate the possibility of a corrupted BIOS being the problem.
Disconnect the power to the desktop and then remove the coin cell battery from the motherboard (see the service manual how to do this -remember which way the battery was installed for when you have to reinsert it, normally it is +ve on top as marked on the battery) . Press and hold the power button operated for 15 seconds and then release. This will force the BIOS back to its default settings.
Reinsert the coin cell battery, reinsert ram into slot 1 only, reconnect the power to the desktop and turn on.
If it now works OK then try all slots. If it now all works OK, you may have to go back and check if the coin cell battery is OK. If the battery voltage is <2.5V DC replace it. The battery type is marked on the battery. It may be a CR2032 which is commonly available. This battery maintains the BIOS settings when the desktop is turned off and when it gets low sometimes the BIOS can become corrupted which can cause all sorts of strange things to happen