iPhone 4S turning on for 5 seconds and off NOT BOOT LOOPING

Hi all,

This is going to be very descriptive so please read all.

I bought an iPhone 4S marked as faulty. It was known to have smashed screen and stuck on an iTunes screen. I repaired the screen and that was working 100% fine. I then went to charge it (I have 3 batteries, 1 original iPhone battery what was 2 years old, but still worked, I have a eBay battery what worked perfect on another iPhone 4S I had, and I have the battery what looks like a replacement one what came with this iPhone) I managed to charge all three enough to get to the recovery mode screen, I don't think the seller realised that it was simply getting it out of recovery mode. I used RECBOOT on my iMac and I got it out of recovery mode but after that it ended turning on for 5 seconds and then just switched off. It cannot be a battery problem as 2 what I used worked on another iPhone 4S, I do not own that other iPhone anymore, and I am guessing the iPhone what I bought, battery does work as well, as its working the same as the other 2 what definitely works. Can I point out its not boot looping. After that 5 seconds you have to press the power button again to get the apple logo on. One more thing, the power button does not work as the connector what reads the home button on the charging port is damaged looking at it. So I can't put it in DFU mode or anything else. Is it best I buy a new charging port so my home button will be read and works?

Think thats everything, hope someone can help.

Thanks, ADAM