.. looks like your log files may be to big.
Try documenting the ownership & perms of the current log files (cache.log, store.log, access.log) & then deleting & recreating them, for example from /var/log/squid:
[root@kryten squid]# ls -la *.log
-rw-r--r-- 1 squid squid 2569753 May 31 21:41 access.log
-rw-r--r-- 1 squid squid 1473 May 29 04:09 cache.log
-rw-r--r-- 1 squid squid 3410485 May 31 21:41 store.log
rm -f *.log
touch access.log
touch cache.log
touch store.log
chown squid:squid *.log
chmod 644 *.log
service squid start
If this works then it looks like the squid log file grow too fast for the logrotate cycle.
This logrotate issue has been answered before on the forums so just search a bit.
HTH