Will apple update my iphone (3g) for free?

Since my computer won't let me update my iphone saying that it is inactive/error or something, i have pretty much given up. I kinda want instagram pretty bad but i haven't updated my iphone in 3 years, the ios is not updated enough to let me download instagram or any current app in general. My facebook app is so outdated and there's so much features i can't use. Will apple update my iphone for free or will they charge me a fee? And are they even willing to do so?

Added (1). I don't even think my iphone is an ios 4.1.2. Its mostly likely an ios 3.

What to do about this girl?

As long as there's not something physically wrong with your iPhone, I'm sure they'd do it for free.

Get an iPhone 4! It amazing and gets iOS 7!

I have the same problem with yours! My iPod Is an IOS 4.1.2 and I needed it updated to the IOS 6.1! All I did was download the NEW iTunes and enter my apple ID! If you would like to keep all your
personal information and apps including songs, go to this website https://discussions.apple.com/...0&tstart=0 and it will help you continue with the rest of your problem

I carnt up date my iPhone 3G it's says iOS 5.