Ok. I have had this happen to me a few times with a couple different PC's/monitors. One thing that is real easy to do and it did fix the problem for me once, is to have the monitor turned on, and then boot the PC up. If you still get nothing, then shut the PC down, and completely unplug it and the monitor. Leave it unplugged for a minute or two. If they are both plugged into a surge protector, then just hit the reset/off switch. Then boot it back up with the monitor turned on. Sometimes a new monitor is just stubborn and won't let the motherboard detect it.
If that doesn't work, it's possible that the motherboard might need the drivers updated on it. It is an older PC, so i'm thinking that could have something to do with it.
Have you had the new monitor plugged into the PC it came with at all? It could be DOA.
Lastly, when/if the monitor still doesn't show anything after the PC is booted up, check to see if the HDD lights are lit, and stay lit. (It will blink off an on, thats normal. As long as they stay active.)