Car wont shift/start

94 honda del sol, manual, 4 cyl. I was recently given this car, it has 120,000 miles on it originally, but it also has a new engine with about 600 miles on it. There are two major problems that both occurred on the same day: First, the car would not shift into gear when I started it. I turned the car off, and it would shift. I started the car while in first (foot on clutch) and it drove ok. Later that day, my battery died. I let it charge after I jumped before trying to drive it. It grinded really bad when I tried to shift into reverse. When it was finally in reverse, the car stalled out when I tried to drive it. I went to start it and the battery had already died. I pushed it out in neutral, jumped it, and when I drove it home it was reluctant to switch gears. Now that its home, it wont hold a charge, and it wont shift gears when the car is on. Is this a clutch problem, a battery problem, or both?