Whu-oh, that does kinda sound bad, but deleting thing under the /var/log/ directory shouldn't have this kind of effect. Now, if you deleted everything under /var, that's not good at all...
If I were you, I would (backup needed stuff first and) just reload it to ensure that whatever issue is causing the missing functionality is covered (and, in the future, if you need to clear off logs, putty in and pick off the logs a bit more manually to ensure you don't shoot yourself in the foot). You could very well be able to detangle this, but it'd take quite an effort (likely moreso than saving needed files and reloading/redoing the setup)
Installing Smoothwall to a VM just to check things and just make sure I'm not talking out my ass
UPDATE My assumptions about Smoothwall were correct: something else terrible musta gone wrong when you went to clear out the logs, I would save off the settings and reinstall (using those settings when reinstalling)
Sidenote: I had never used Smoothwall before (had been a DD-WRT and Tomato user, I now roll my own proper server based on Debian that pulls router, firewall, torrent client (yes, torrent client), email/webmail, web server, and general remotely-accessible duties), but it is very nice and I now I have an excellent suggestion for friends who are looking to setup a bit more than one of the alternative router FW setups but isn't quite ready for a full server setup (it's tricky, you need to keep the system updated, and watch for constant attacks)