@cicerone imposter,
Furthermore, if this the issue with the monitor:
1. Is it "winking out"? Dimming or losing brightness is one issue, but total loss of power is another. Does the monitor shut off (no power led light).
Also, you may have a bad power cord or bad conenction to the power strip when you had plugged it in where and when it was hooked up to the Dell. Now you hook it up to HP, you might not see the problem again.
Is this not happening at all now to the monitor? You may accidentally found the problem. You could have a bad outlet at the power strip, bad connection to the monitor or a bad video cable and/or connection to the Dell.
The key is what happening now with the monitor, seeing that the Dell may not actually be the culprit?