TL16C550 UART doesn't transmit, baudout is permanently high
Possible causes:

The MR pin is high (master reset)
Have you put your scope on the MR pin? This should be low for normal operation.

The Baud Rate Generator has an illegal value
Have you verified that the values written to the BRG?

The BAUDOUT pin is being pulled high.
Are you sure the BRG pin does not have a short circuit?

The UART certainly does not disable the BRG depending on any of the modem control signals.  Either the oscillator is not running (and you state that it is) or the BRG is in reset, or the pin is externally driven high/low.