NAD M33 issues, don't know where to start

Don't have a NAD myself, but one item you might check is to remove the case cover and see if all the connections look right.  Computer display screens are typically plugged into the mother or video board using a flat ribbon cable.  Yours may have worked loose.  And check the connection at the display end of the cable, too.  Finally, note the ribbon cable may not have an actual "plug" on the ends, but rather just a stiffer section of cable with silver or gold connectors. They slide into a female connector on the circuit board that has a up/down slider that moves maybe n 1/8th of an inch to lock it down, so are a little trickier to use than a normal plug.

Ouch.  That's a pretty new unit to be incurring that type of repair charge.  I did consider this model.  

I had the exact same problem. Sent it back to NAD under warranty, they sent me a new one although it took 6 months!

How is the sound quality of the M33?  Are these quality defects isolated or common?

I had one for while and found it kind of un-engaging.  Great bass, takes control of the speakers but (for me) it just didn't do it.  Sold it and replaced it with a Gold Note IS-1000 which I much prefer.  No cool display, but the tone seems much richer and the presentation really hooks me.  FWIW.