1. What's in the file "Exit.log"?
2. Is the log directory set in QVS really the one you are looking at? For those settings to apply, QVS will need to restart, which would explain the "Exit.log" (I'm guessing) and the subsequent lack of further logs. Check in the QMC.
3. What's the last couple of rows in the last event log?
4. Is the QlikView Server service running?