Wheels lock up - 2001 Triumph Triumph Bonneville

https://www.youtube.com/watch?v=d9dEOtFgKDc
Method 1 Unlocking Your Steering Wheel

1. Insert the key into the ignition. ...
2. Turn the key gently. ...
3. Apply pressure to the steering wheel. ...
4. Do not shake or rock the wheel. ...
5. Pull the key out slightly before turning it. ...
6. Turn the wheel and the key at once to unlock it.

https://www.wikihow.com/Fix-a-Locked-Steering-Wheel

Cause!
One of the most common reasons why a steering wheel won't lock right is that the detent is broken or worn down. If you don't know what the word detent means, then don't worry. The detent is basically "the catch" part that makes sure that your steering wheel locks into place.
https://carroar.com/steering-wheel-wont-lock/

Wheel Bearings

Print
Adjustment

2002-05 Models

1. Before servicing the vehicle, refer to the precautions at the beginning of this section.
2. Remove or disconnect the following:
   
   Rear wheel Brake drum Hub cover Cotter pin Lock nut cover
3. Adjust the locknut to achieve wheel bearing play of 0.001-0.006 inches (0.025-0.152 mm).

Removal & Installation

2002-05 Models

1. Before servicing the vehicle, refer to the precautions at the beginning of this section.
2. Remove or disconnect the following:
   
   Rear wheel Brake drum Hub cap Cotter pin Lock nut cover Lock nut Wheel bearing retainer washer and the outer wheel bearing Hub assembly Grease seal Inner wheel bearing
3. Clean and inspect the wheel bearings and races for unusual wear or damage. Replace parts as necessary.

To install:

1. Pack the wheel bearings with grease for assembly.
2. Install or connect the following:
   
   Inner wheel bearing Grease seal Hub assembly Lock nut. Adjust the locknut to achieve wheel bearing play of 0.001-0.006 inches (0.025-0.152 mm). Lock nut cover Cotter pin Hub cap Brake drum Rear wheel
   

The wheel (all theft and safety) locks are connected to other components. They are on shifter, brake, and steering wheel. Try putting vehicle in neutral and with foot on brake see if it will start like that. It may just be a little off for wheel, brake, and shifter to mesh and lock up. They all have a say in how it goes. If vehicle is on hill of any kind it can keep locks from going, if wheel is turned to odd spot, or lock from shifter is off, they can all keep system from locking up. Would guess that it is not starting because one of the neutral safety switches is not engaged and wheel lock is kind of a side affect of this also. If you can take key out of ignition but wheel is not locked there is clearly an issue with the lock up system. But the wheel lock points are not at every inch of wheel turn. Sometimes you turn vehicle off with wheel at a point a little off from one of the holes and you just turn wheel a bit and lock will engage. But try starting in neutral - try moving shifter all the way back and then into park (with brake pushed) and see if they will get back in sync. You may have to push / roll vehicle a little to get weight off shifter and wheel, but if shifter moves from park with no brake, or key comes out with no wheel lock (or with shifter not in park) something in the 3 way lock system has come out of sync.

No, an abs sensor only senses the speed of the wheel. When one wheel locks up or is running considerably slower than the other wheels during braking the ABS system will reduce the braking power to that wheel to stop it locking up, hence the term Anti Lock Brakes. This happens in milliseconds. The sensor itself cannot lock a wheel up.

could be 2 things bad smart key and probably shift cable disconnected under steering wheel

move wheel side to side while trying to start -if starts and wheel is still in locked position problem can be pin cam that fits into slot on wheel may have broke which would require dis assembly of the wheel to manually move and repair lock

if the steering wheel is turn all the way one way and locked by the steering wheel lock then you will have to turn the steering wheel more and try turning the key.sometimes when the steering wheel is turned all the way one way and locked the pressure that is against the lock will sometimes not allow the key to turn.if the wheel is in the straight ahead position it may be the ignition key lock is worn and needs replacing.

If the steering wheel is under pressure (can happen even with the wheels straight ahead) the lock mechanism can be putting pressure on the key making it very hard for the key to release the lock mechanism. Try pulling on the wheel in one direction and turning the key. If nothing, try turning the wheel the other direction and try turning the key. You may need to replace the lock mechanism. This usually involves being able to turn the key in the lock or having to drill the lock. You are probably going to need a locksmith for this one. You will need a replacement lock cyliner mechanism if the locksmith has to punch the lock.

Although the car is not in front of me, it sounds like when you park ( is this parallel parking ? ) your steering wheel is turned hard to the left or right, which creates extreme pressure on the steering wheel lock. In order to help overcome this problem, you must "armstrong" the steering wheel in the same direction the front wheels are turned. Locking up on the freeway with this same issue. Highly unlikely.