I belabored over this for a while as well. I replaced the mast, but two weeks later it was getting stuck again, so I just installed an interior power amplified glass mount antenna behind my rearview mirror. And I did nothing regarding the wires going to my power antenna because I didnt need to

I just plugged the power for the new antenna into the black wire that was powering the motor. (behind the radio console)
You, however sound like you are in quite the pickle having cut wires. You are going to have to run an antenna cable through your dash now if you keep it fender mounted...I haven't tried, but Ive heard and read splicing that is not effective.
So you have a few options -
You can reconnect power to the motor, buy a new mast with the nylon teeth and feed it in, and deal with the cut antenna wire.
You can do the Tacoma whip antenna mod which is non retractable and therefore needs a different base in the wheel well to attatch to
Or you can go with a similar solution to what I did. Grand total on mine was $32. Labor involved removing my roof console to ground it. Removing radio bezel to get to plug it in and give it power, and then I just pushed the wire into the headliner to windshield, down dash and then under over to radio. I had to buy a 2' extension cable at Best buy for $7 and some change which I didn't mind because you cant see the cabling AT ALL in the interior - I took the long route to hide it, and therefore needed the extension.
If you go interior, you can either buy a $4 antenna hole plug at the stealership (its on the blowout of the fender well liner parts page) or you can just retract the antenna into its current mount and leave it alone.
Good luck!