Transmission Question: Grinding when changing gears. What could this be?

to determine if the transmission is shot would depend how long you have been driving the vehicle with this noise going on. it sounds to me like a mix of things i thing one of your bearings inside the actual gearbox went and it left play in the gears. which eventuall let the synchronizer get chewed up. with a synchronizer chewed up this would lead to gear teeth being worn down, chipped, snapped off etc. which would explain why your first gear is so slow to accelerate. it doesnt have the grip it used to have. i would take it to aamco and let them look at it if there is one near your house. explain the issue. but more than likely if you have been driving it awhile like this youll need a transmission anyways. mind you that this is only my opinion i would have to look it over and listen to it to be certain. but im almost positive your gearbox is pretty well shot