There is possibly more broken, because you also get
Unable to open logs
First of all, enable more logging
Check your file permissions in
I use often following command to debug:
strace -f apache2ctl start 2>&1|grep -v " ENOENT " | grep -Ee " E[A-Z]+"
It shows you excactly which calls are failed.
Another reason could produce overlapping listen adresses like:
Listen *:80 Listen 126.96.36.199:80