I am using a damaged Viewsonic LCD monitor I purchased inexpensively.
Portions of the display are distorted or dead and it looks like the
glass is cracked in the corners. I know that the previous owner took
out the display panel in the hopes of building a projector and later
put it back in.

A friend of mine is convinced that using the monitor in this state is
emitting excessive harmful radiation. Is it true that a broken panel /
cracked glass will increase the radiation output? Is it dangerous?

I know there are "zero radiation" LCDs, but they only talk about
reducing magnetic radiation, which I wouldn't think would be affected
by the glass panel, but I don't know enough about electronics to be
sure.

LCD flat panel has radiation too.
please reference RoHS (the Restriction of the use of certain hazardous
substances in electrical and electronic equipment)
standard.http://www.rohs.gov.uk/
lcd panel contains Pb and Hg in Fluorescent lamps,High Intensity
Discharge(HID)lamps,painting or pigment or link, LCD back light and so
on.

if you using cracked panel , it's Liquid Crystal will have more volatilization.

So, please careful!!!