iPhone wont charge or connect to itunes or computer or wall.

Ok i have a little problem with my iPhone 3gs. At first my screen broke so i ordered a new one and put it in, and my phone worked just fine for about 2 days. Then it stopped charging with my wall charger. At first i thought it was just the charger cable. So i hooked it up to my car charger and it worked for about 10 minutes and stopped again. I then tried multiple chargers and ways of charging and none would work. So i figured it must be the charging components inside the phone so i ordered a new one along with a new battery just in case. I replaced both and plugged it into my computer, and it popped up and said it was installing the driver and said an iPhone had been found. Then within 10 seconds it disappeared. Then i was holding my phone and squeezed the sides a little and it started again. So there is the problem. There is some kind of connecter or something that’s not doing something right for it to charge or do anything via the charging port. I have looked all over the internet for different posts or anything relating to it and i have found nothing at all. Any help would be great! Hopefully someone has had a similar problem and found how to fix it. Thanks in advance!