Laying it down is fine so long as its done carefully. I've transported loads of cabs in my Estate Car laid on their back and not killed one yet.
Make sure there aren't any protrusions, brackets etc sticking out that are going to get bent/snapped/pushed through the back when you lay it down.
Open the cab up and make sure there's nothing loose inside that will move or fall when tipping it. Generally the only damage you can cause by tilting or laying a cab down will be caused by loose coins, screws or components inside crashing into other stuff inside.
Take ropes or strapping to secure it to the bed. Ideally stick some thick cloth under all the contact points to prevent scuffing. Make sure its secured from sliding backward and forward as well as side to side. I usually lay a blanket down first so the T-Moulding doesn't get scuffed when sliding it in or out.
Really though, just use a bit of common sense, keep it slow and steady and make sure you've got enough help on hand to load and unload it easily.
The only possible issue I could see with a monitor would perhaps be regarding polarity and it needing degaussing when its put back upright but AFAIK most post 80's monitors do this anyway without having to go all Harry Potter on them.