Take the key out and turn the steering wheel.
The lock should usually engage after about a 1/4 of a turn starting with the wheel in the straight position.
If you can turn the steering wheel 1 full rotation with the key out, then it obviously doesn't work, and that's the "play me for a fool" test.
This might be easier to achieve with one side of the car jacked up to reduce friction, but not impossible with both wheels on the floor.
If the lock doesn't engage, then you're either going to have to let someone have a look at it or get your hands dirty.
I'd personally be tempted to try and fix it rather than replace as you may end up with different keys.. one for the doors and another for the ignition.
Getting the lock off could be tricky as they will have shear bolts.
Bolts which are designed to shear the head off once they are tightened up.
This is supposed to stop a car thief coming along with a socket set and just removing the lock, which of course makes the job difficult for someone taking it off legitimately.
If you don't have a few hours to spare, have no idea which end of a screwdriver is the pointy end, and have no practical skills, then £140 isn't a bad price.
unless you're like me and hate the fact that of paying someone £140 to do what I could do for myself for nowt.