So, what we know so far:
1. CPU - Ryzen 3 3200G
2. Motherboard - Gigabyte GA-A320M-S2H-rev-1
3. Case - CIT 1016 Gloss black micro ATX PC computer
4. PSU - 500W that came with the case
5. No discrete video card
6. RAM - 2x 4GB DDR4 PC4 2133p (P/N: 798033-001)
7. Monitor - Avanhard XM19A, has one D-Sub (VGA) and 1 DVI port.
8. Connected with D-SUB (VGA) cable
9. On power on fans are spinning, lights turn on, DVD drive opens/closes. Nothing on monitor!
10. Monitor works fine with OP wife's computer.
11. Monitor works fine with a neighbours computer. We don't know which connector was used!
12. OP computer connected to a naighbours monitor behaves the same as with his monitor - no signal. Again we don't know what cable (VGA?)
Assuming VGA cable was used with naighbours and wife's computer it would mean that cable is ok.
Still can be checked with DVI if OP has or can borrow a cable.
RAM is not on compatibility list and we know Ryzen is picky about memory. Maybe it is a problem.
Seems there is no speaker/beeper in the case, hard to tell from case info I found (i.e., no info about that detail).
Stumpy can you double check if there is no speaker on the front of the case (from inside) and if any cable in the bunch has speaker written on connector?
Maybe it is a BIOS issue. Don't know if it is possible that it may be set to use discrete graphic instead of on-board but there is none?
You can do as blobster said or use CLR_CMOS jumper on motherboard.
If you want to use CLR_CMOS
turn off computer, unplug it from the wall outlet and connect two pins marked below with metal object for few seconds.
