Water damaged iPhone 4S, screen not working

My iphone 4s was dropped in a cup of tea by my one year old. I put it in a bag of rice for 48 hours then sat it in front of a dehumidifier all day, but it wouldn't fire up.

Today I followed the instructions on ifixit to strip down to the logic board, soak it in isopropyl alcohol and clean all connectors. In removing the logic board I ripped the ribbon cable from the power button to the logic board, but decided to try reassembling as is to see if anything was working.

To my surprise when I plugged it in it made a charging noise, and proceeded to heat up as expected when charging; however the screen remained blank. On connecting to my mac, iPhoto was able to see it and import photos. iTunes recognised it as my phone and was able to sync, although I could not back it up as it is locked with a pass code. It even rang when I called from another phone, although without the screen working I could not answer. My questions are:

1. Obviously I will need to replace the power button or ribbon cable. Does anyone know whether the missing connection could cause these issues, or does this suggest an additional problem with the screen?

2. I haven't tried removing the screen, but reading the instructions it doesn't sound like there is much I can do to repair the screen other than replace it. Or are there any accessible points I should be trying to clean, other than the connection to the logic board?

3. Most instructions suggest replacing the battery, although it seems to me to be working ok. Does this sound like it needs replacing?

I'm trying to get the phone to limp on at the least cost I can as I'm planning to buy a 6 when they come out so don't want to spend a fortune fixing this up for a couple of months.

Many thanks