Welcome to iMore. We'll get to the bottom of this. I love a good conundrum.
I think it's driver based as I had the same issue on my computer although it did work on another computer. Both of mine are WIN 7 though. Bear in mind that the iPod is a totally different animal to the iPhone and it only takes one little driver error to make it not recognise one over the other.
I uninstalled and reinstalled iTunes, including every instance of an Apple driver or product on my computer (So, Bonjour, Apple Mobile Device etc) and reinstalled it all and it fixed the issue
Do you know someone else with a similar iPhone who you could ask to connect to your computer to see? It would certainly help in narrowing down the problem then by highlighting exactly where the issue lies.
If it's a brand new iPhone, it's possible that you haven't yet added in all your accounts or signed into all the apps you have yet, so erasing the device and starting again might be an option of last resort too.
And lastly, my condolences for having Windows 8.1.