How do I get my non-jailbroken unlocked iphone out of restore mode without using itunes?

I've spent hours searching the internet for a solution to my problem but nothing has worked and it is a pretty uncommon problem. My iphone being in recovery mode is the third in a series of problems I've had with my iphone. First of all, I'm in a third world country where the internet is very slow and I've noticed itunes will not connect to the internet unless it is fast.

My iphone does this thing where it turns off even when the battery indicates over 30%-50% power. This happens more frequently when the service fluctuates or I try to take a picture or something. In January, I selected the option of encrypting my backups and backed up. Later, I deselected this option and then tried to backup but it would never complete. I couldn't sync either until I started exiting the backup process from windows tasks. Then it would skip to the sync and after show a message about itunes not being able to backup on this machine. So I haven't been able to backup in over 2 months.

Recently, my iphone did its turning off trick and as I tried to turn it on holding the power button, it entered recovery mode. The best option would be to go through itunes, but as I stated above, itunes will not connect. I've run diagnostics and although it picks up the internet connection, it says itunes cannot connect safely etc. I've run tinyumbrella and dr.phone's wondershare with the same result: My iphone just restarts and goes back to the restore screen.I need a solution that doesn't require a fast internet.

My iphone is 3GS 16GB and I updated the iOS once after 6.0. There was a prompt for a new version that I never updated to.