why itunes cannot recognise my ipad mini retina ios7 on windows 7 64-bit?

I have recently bought an iPad mini with retina display - iOS 7 and when I connect it to my computer, there are several problems:

1. iTunes does not recognise it. At times I do get an error displayed that it is not able to connect to the device.

2. the iPad display says it is not able to charge from the computer USB.

I have had problems before with this computer and my iPhone 4S as well as my new 5S.

It was always able to resolve it by reinstalling the driver and or following the instructions to reinstall iTunes.

I have tried all of that several times now and it is simply unable to recognise it. I can open it on My Computer, which means I can download the pictures of the iPad, but I can't put music and other items on it. And I cannot make a backup of the apps that I have installed etc.

Any suggestions? I have had for a week now and have not been able to successfully connect even once!

Windows 7 Professional 64-bit, desktop PC

iTunes 11.1.3

iOS 7.0.4

I would also like to configure it for wifi synching but that is only possible if I manage to connect it successfully via the cable at least once.

Note: the cable is the original cable and I tried it with my iPhone 5S cable as well (just in case it's the cable). Also tried every one of my 6 USB ports on the desktop (4 USB 2.0 and 2 USB 3.0).

I'm at wits end. Please help!