Was it shifting like this when you got it or did it just start? Was there ever a tune done to the car? If so did you get the tuner, was it put back to the stock tune? Have you verified the fill level yourself? How does your buddy KNOW its good? Computer will only tell so much, it very well could be shot inside somewhere and the sensors will still say good.
Could it be a messed up converter? Did you try a new OSS sensor (I doubt it is this but you never know)? Could be a number of things really. The good news is that these transmissions are cheap but just to let you know, since you have an 04 you will ONLY want a transmission out of another 04. The 2004 was the only year to get the 4R75w vs the 4R70w from 96-03. The 4R75w is much stronger plus you'd need to change your OSS pulse number via a tuner from 24 to 6 to run a weaker 4R70w. Not a big deal but just more asspain for a weaker trans=not a good idea.
Hope you get it all sorted out, like I said if it is the trans you can often find a good 4R75w for $300-$800 depending on mileage and location. If you buddy has a shop see if he can hook you up with an install for a few cases of beer or whatever. For a shop with all the right tools a trans swap is literally a 2-3 hour job. I can drop the manual trans out of my car myself on a lift in about an hour once the car is in the air if that says anything. About another 1-1.5 hours to put it back.
2000 Mustang GT Steeda #0048
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.