This issue is one of the main reasons I actually have a 5s. Video chatting on iDevices is embarrassingly simple. That said you've got good solutions like Google Hangouts and Fring, amongst others.
Surprised you're having issues with Skype. I've installed that on all my pcs with no problem. I have Windows 8 on my desktop and Windows 7 on my netbook. I installed the exe from Skype's website and not the one from the Windows store. Wonder what the issue is?
Hangouts works really well too. I think Yahoo messenger does video but I haven't used that in a long time.
Skype works, Hangouts is sorta ok too but you have to use a plugin with Chrome on PC, so Skype is the better choice (but don't use the Windows store version, get the desktop version from the website).