Cindy, in your case, since your monitor "works fine" on other computers two questions need answers.
Did you (#1) leave it on these other computers long enough for it to warm up to it's normal operating temperature?
And did you (#2) use the exact same settings on both computers?
If yes to both, then the monitor is probably ok, and the video card is suspect. There is a faint possibility of a grounding issue between monitor and PC if they are plugged into different AC sources, or if the power cord to either has an "open" on the ground wire.
However, a No to #1 means you didn't eliminate the possibility of your monitor having a heat problem (bad monitor).
And a No to #2 could mean that the stored set of adjustments for that particular density/frequency combination are incorrect. Each pixel density/refresh frequency pair has a unique set of adjustments stored in memory inside the monitor. Unless you used exactly the same settings on both computers, your "test" is suspect.
If they were the same, suspect the video card, if not, retest at the same settings, or use the settings that worked on the "other" computer on your computer, and if that works, and satisfies your needs, know that the monitor is on it's way out, but that you may be able to get more life out of it before it finally dies.