Old Computer Display Problem

There's not much that can be said just from that other than the card may be dead. Or the monitor if you haven't tried it on another. Theoretically it could be an issue with the motherboard as well.

I tried it with two monitors and I tested one of them

Probably the motherboard's PCI or AGP slot is dead. Nothing much you can do about it.

Basically you need to swap parts, which can really be a pain however that's all you can do.

I'd do it in this order:
1) Graphics card
2) Power Supply

It may be something else but start there and get back and I'll help if possible.

*You can also confirm the graphics card by trying it another computer. AGP is roughly 10 years old and was replaced by PCIe (PCI Express). Any PCIe card will work in any PCIe motherboard as long as the Power Supply is adequate.

The same goes for power supply. The PSU need not fit in the case to test it. Modern PSU's have 24pins on the motherboard input and older motherboards use 20pins, however most (or all?) of the modern PSU's can unhook the last 4 pins for compatibility.