Won't start/key will not come out of ignition

Hello;
This is my friend's vehicle and I was with him last night trying to figure this out:
He installed a new starter/solenoid, but still won't start. He has a charger on the battery which said it was at 100 %, after a few turns of the key, the battery dropped down to 7%. I say it's the battery not strong enough, as the first few times it just clicked, then nothing. He says the battery is only a year old, but I said if your alternator is not charging, then the battery will eventually die. I checked the starter relay, which is the same relay for the parking lights. (Swapped them but no change) and parking lights work, so I know the relay is okay. I heard that there are fusible links just before the starter. Is this so? He also said that the tow truck driver tried giving him a boost, but still nothing. He did however, bypass ignition, etc. And just jumped the starter direct from the battery and it did start. Maybe the new solenoid is bad? Maybe a bad wiring connection?
Also, he cannot remove the key from the ignition. The shifter does move with the switch in the on position and the foot on the brake, but even though it goes all the way into park, the key won't go all the way back to lock and cant be removed.
Any input you have woud be greatly appreciated! Thanks, Jim