Stuck in park position

PARK IS DEAD,BUT LEVER SHOWS PARK
BAD SHIFTER OR BAD LINKAGE TO IT.
BAD CABLES. THIS IS PURE PHYSICAL MECH. FAILURE
NO MAGIC COMPUTERS,
L

The emergency brake would be the first thing to check.
It is also possible that one of the brake shoes are stuck in the on position because of excessive oil in the drum. A brake caliper may be stuck in the stop position. Also check to see if something in blocking one of the wheels.

Don't know about needing the brake pedal pushed to get INTO park, but it might, as the pedal needs to be pressed to get it OUT of park.

Bad electric motor.

Sounds like the module is bad.

There is a magnetic switch on the 'park' position. The car only starts or releases the key in 'park' is enabled. Maybe this switch is not working! Try to replace it!

On this website you find information (diagram, description and location) about fuse boxes in Cadillac XLR (2004 - 2005)

Cadillac XLR 2004 2005 fuse box diagram Auto Genius

sounds like possibly the transmision linkage has gone out of adjustment and vehicle is not completely engaged in park. Have seen this on many vehicles

The most likely problem is the locking mecanism in your shif selector.
There is a selenoid that prevent the car from get it out of park unless you push the brake pedal while the car is running or the ignition switch is on.
The problem could be in the brake switch itself under the dash or the selenoid in the shifter console.