I'd take it inside, unpackage it, and see if the monitor itself feels wet/damp at all - maybe check the screen for signs of condensation/moisture. Just to be sure, let it sit for several hours in case it needs to dry out - then give it a try.
I found
this monitor testing page; near the bottom there's a button "Launch Calibrator"- it's a small battery of tests for the monitor. You can use Alt-F4 to get out of the page....though I did just find the Exit button: hold the cursor over the Monitorsdirect.com on the upper left of the testing window screen. The Exit option appears below it then.
Oh yeah, what carrier was this? FedEx, UPS, Airborne Express...
I had a monitor delivered by FedEx once. The guy didn't leave it on the doorstep, and I was rather annoyed by that, since they had my signature waiver thing on file, plus I was home at the time - I just somehow didn't hear the doorbell. Well a little bit later, he came by again to try to deliver it again - he said it looked like it might rain, and the box was labeled that it held a monitor, so he didn't want it to get wet. I was a good bit less annoyed then.

So there are at least some good, responsible deliverypeople out there.