Typical 450W PC supply will have two 12V rails. One will be on the 4/8 pin ATX12V header which is used to power the CPU, and the other will be on the main ATX header as well as the disk drive connectors. Each will likely be capable of supplying 10A or more.
Given that the PC can run off a 160W PSU, I doubt the mobo/CPU draws that much. If you only have 1 HDD, you should be fine from a power standpoint.
If your mobo does not use the 4/8 pin ATX12V header, I'd go ahead and use that for your monitor. That will give it a dedicated rail. If the mobo does use that connector, just use a disk drive connector. Use big wire (at least 18AWG) as 4.5A is a fair bit of current, and voltage drop on smaller wire will become apparent fairly quickly.
Just watch out for ground loops. Some devices intended to run off isolated "brick" type supplies reference their incoming power to strange places, which might result in a ground loop with the PC via the video cable. Melting and/or smoke would ensue. I've not known LCD monitors to do this, though.