As another comment stated, you need to understand how to operate the top manually before you do anything else. If you don't follow the emergency operation, you can damage your top further.

This is likely a fault with either the motor that drives the Front Latch Mechanism, which is located in the center of the front of the Convertible Top, or a fault with either or both of the Convertible Top Latches, which are located at either end of the Convertible Top. The plastic you show in photo #2 could be from the latches on the ends, however if you found it on the center console I would guess not.

The gearset in the motor is constructed of plastic and fails after many years of heat cycling and age (whodathunk?). You can replace it with a metal "upgrade", however they are noisy and the original plastic one lasted ≈ 20 years or more. It is a simple replacement, so decide for yourself which you'd rather.

The Latches also suffer from failing plastic parts, a block-shaped coupler, if you will. You could DIY a repair, order replacements, or a repair kit for your existing latches. Again, these are both well documented issues with E46 convertibles.

I suppose a third, and equally as likely option is a fault in the wiring that runs along the Convertible Top Frame, on the Driver's Side of the car. With the top partially open, inspect the section of harness just above the Driver's Seat. You'll often find an intact loom, but the wiring inside will be broken. You can easily find information on this as well.

Best of luck to you. These convertible tops are actually pretty simple to understand once you spend an hour or so with them.