1996 Honda Accord Car wont start

So I recently replaced the starter and starter solenoid because it was having problems starting. They checked it at autozone and said it was bad. So I replaced it and the car started fine. But then two days ago I went to the store and when I left my house tha car started fine. But after leaving the store the car wouldnt turn on. I tried it a couple of times. I tried to turn it on on neutral, checked the battery terminals, taped on the starter and it still wouldnt start. So I called my dad so he can bring some jumper cables because I thought the battery was dead. When my dad came he got on and it started with him. He said he pushed the shift stick foward and turned the key and it worjed. And today we were going to pick up my sisters car from the shop and it wouldnt start again so I did the same thing with the gear stick and it worked. So my questio is what is wrong with my car? Is it the gear box?