Hello, this will be my first post and concerns a technical issue with my car.

Unfortunately, I seem to have a few issues with my 1992 Honda Prelude.

To begin, the car shakes when it is driving but not when it is in 'Park'. I recently had the engine and transmission replaced (both were from Japan) from a reputable dealer. The car shook before I changed the transmission and engine from a F22A1 to a H23A1 model. At one point my mechanic did mention that my front motor mount was broken but should have since been replaced. If it hasn't been replaced, could the front motor mount being cracked be the problem?

Additionally, the cars pulley belt seems to have fallen off. I picked up the car from the mechanic in what should of been drive-able condition but after a few blocks I noticed a sound like something was going to snap off (probably the pulley). This leads to the second problem:

The car will just go dead from no battery charge after only a few minutes of driving. I am not sure why this is but I do know the problem is made worse when the lights come on. After the lights come on it is only a matter of minutes before the whole car shuts down. The battery is new so I'm not sure what the problem is. Could it be that the alternator, that came stock with my F22A1 model engine cannot supply enough power to the new H23A1 model engine?

Also, the 'D4' light keeps flashing on my dashboard which signals a transmission problem. However, the transmission has been replaced with a working transmission. My mechanic mentioned that this may be because the original computer is still in the car which may still be reflecting a transmission issue when, in fact there is not one. Is this a correct assumption on his end?

Any help is greatly appreciated, I'm all out of money and have had the car in the shop for three months which has put a huge burden on me for work and school. As such, any help and pertinent advice is welcomed.