Used KT1006, rebuilt battery, no lights or engine

Your transmission has failed. Not uncommon for a car that is 12 years old, especially if the car has ever overheated (since the transmission fluid is cooled through the radiator). Take the vehicle to a transmission repair shop, and they will likely recommend replacing the transmission with a rebuilt one.

Sounds like a bad alternator

Sure it can be rebuilt as long as the block is fine,It might be more cost effective to purchase a low mile engine and drop it in. Engines and transmissions are widely avail. they built a lot of these cars...

Do a web search or find an appliance parts or service place as they usually have rebuilt timers or youmay luck out with good used one OR bite the bullet and get a new one or used ones usually go pretty cheap also.

I assume you have the Lithium slide batteries, if so the most likely problem is faulty batteries, Makita had a high failure rate with these batteries, take them back with your proof of purchase and it is quite likely they will be replaced under warranty

Lets start at the beginning.
If the engine is locked now, and you drove it with no oil in the oil pan, the engine is probably toast.
You could have it rebuilt, but it would be cheaper to get a used engine if you can find one with less than 100,000 miles on it for a reasonable price.
You are talking about spending $1500 or $2000 to get a used engine installed and the car is worth around $2000 in good condition.
The question would be, how long do you think you can drive it after it is fixed ? Two or three years to get back that investment ?

Hi:
This sound is an indication that the color wheel is faulty in the light engine, with mits sets you must replace the entire optics engine. You can purchased used light engines or have your sent in for repair. Try this site for rebuilt engines www.tristatemodule.com

Pull-A-Part

We are not a parts service, but try an internet search for used VW parts, there are many VW only wrecking yards, that is your best chance of finding it. Also call VW and see if they sell a rebuilt module.

Problem is once the heads are off you need to have them checka nd probably planed and rebuilt. If the heads are also cracked than you will buy heads. In my area a head gasket job costs around 2-2500$ if it is a v6 15-1800$ for 4 banger. USed engine is a possibility but you can get a bum engine. I vote for sending to machine shop and having rebuilt. Other option is finding an already rebuilt engine and dropping in.
If minor leak you can try alumaseal. Awesome stuff. Is a fine aluminum powder taht fixes small leaks. Major blowouts can't be fixed by alumaseal.