Deleting the logs shouldn't have messed up your USB. I'd suspect a dodgy USB cable and/or socket.
Have you tried Avast GrimeFighter? Safely cleans out old cache.
Also I'd recommend rooting your phone and then install AAT (rooted). With a rooted device you can free up loads of phone storage by transferring Google play services etc from phone storage to SD storage. I believed AAT MUST install to the device memory so it will survive simply the SD card being removed.
The reason I suggested deleting the logs is because Samsung phones seem to report free storage space despite it actually being taken up by logs. They can't be deleted to make space for installing apps. Now, with them not registering in used storage space, I assume the original idea was that they could be deleted to make room if necessary, hence then not showing as using any storage.
I was having trouble installing a 20MB app from the play store despite the Samsung file browser and ES File explorer showing more than a GB of free space..."not enough storage space", it said. I first assumed it was a Playstore problem and did all the 'clear data' in every app that said 'Google' in my apps list. This would inevitably green up enough space for me to install a small to medium sized app and I assumed the problem disappeared with what I thought was corrupt 'cache'.
It wasn't until I did the method I explain above did my problem go away permanently.
