Default [Q] Stock Moto G 8gb won't let me install any apps

Hi, my friend's Moto G 8 gb isn't working properly, every time he tries to install an app it gives an error such as "Insufficient storage space" http://imgur.com/1HcNKyu

even though there should be plenty of space available http://imgur.com/WAjmIwC

It won't even let him upload screenshots to imgur http://imgur.com/80Ihwnb

He bought it a few months ago, it's been having this problem since shortly after he bought it, it's fully updated and running Android 4.4.4 http://imgur.com/98UAlDF

When trying to install programs, such as the very small DiskUsage app, it gives the insufficient space error even if he's just cleared app caches and uninstalled apps, which should definitely have cleared enough space to fit it.

What can we try to fix this? He'd prefer to avoid doing anything too complicated such as rooting or installing custom ROMs.