iPad Air won't sync/charge to PC via USB

Charging via your PC is not the best way to do it for your iPad. Unless your computer has a high powered USB port, most USB ports out there put out just a fraction of the power an iPad wants. iPhones only want half the power that iPads do so they charge fine via USB.

As to the PC not seeing your iPad, I'm going to bet it's a driver issue. Is your iTunes up to date? If not, update it then try again. (Say the last time you plugged your iPad in it was running 8.4, you upgrade to 8.4.1 over the air, your iTunes won't have the right driver for your iPad). Sometimes simply restarting your iPad can help. hold down the sleep and home keys for about 20 seconds. When you see the silver apple, let go and let it reboot and try again.

Sometimes iTunes only thinks it updates the driver. I had a similar issue on my PC and I ended up uninstalling iTunes, apple mobile device driver and apple application support (control panel, add/remove programs), then i redownloaded iTunes and reinstalled it (I didn't lose any content) and then connected my iPad again.

Skydiver handled the charging issue. As to the lack of recognition, what kind of Anti Virus Software are you running? McAfee, Norton? McAfee in particular has been creating problems with iTunes - it did for me until I ditched it. May want to try turning Real Time Scanning and Firewall off momentarily to see if your iTunes recognizes it then.... Reboot your PC in between and the reconnect and test... If interested in more details about what AV can do check this thread out, my own issue... iTunes starts with the Welcome screen every time

What AV are you using? Disabling the firewall after you have installed iTunes will do nothing. You have to disable Real Time Scanning to test.