Going back to the original problem.
If you have to tap a monitor to get it to "work", that is usally indicative of a cold solder joint.
Especially if the monitor is new and exhibited no other signs of failure (e.g. a hissing sound or pop indicating a capacitor blew out, or burning/etc.. indicating a short or defective component)
This COULD be as easy as removing the shell and shields and then with an insulated wood or plastic stick, poking at the circuit boards on the top and bottom while the unit is on, looking for the place where the solder didn't flow correctly and isn't making a solid connection.
However, the others are right: If this is < 90 days old, get it fixed under warranty. If no receipt or no warranty coverage, then check out the above. Otherwise, scavenge it for parts and toss it, or eBay it.
BTW-FedExGround shipping should only be around $25-$35 for a 19" computer monitor. On those massive 21" ones, with the heavy metal double frame and shield, double boxed, only cost me $48 to ship.
I actually shipped a 19" single boxed last year via UPS ground and with a business pickup account it cost about $27 to ship then. And FedExGround is usally less expensive I've seen on higher weight/sized items.