No - assuming you are connected to the internet (browsers work, programs update etc) then that does not look right.
First thing I would do is to make sure that windows firewall is turned on (it is compatible with avast firewall) to make sure you have some software firewall protection (you are hopefully behind a router hardware firewall anyway?)
What previous security software/FW did you have on the machine before AIS, and how was it uninstalled? Did you use the manufacurers dedicated uninstaller in windows safe mode? If not, get it from eg here
http://kb.eset.com/esetkb/index?page=content&id=SOLN146 and do so now.
Then you could try an avast repair - but personally I have never found it to repair anything.
I would remove and reinstall the firewall component.
(i) Control panel-uninstall-AIS-uninstall/change-change-next-uncheck FW component-reboot.
(ii) Then repeat the above but this time check FW component.
If you have ccleaner installed run it between (i) and (ii) until it finds no more registry issues (but that shouldn't really be necessary). If you do run registry cleaner save its changes when prompted in case you need to restore
Let us know if that works.
(If the above doesn't work then you could do a complete unintall/reinstall of AIS (with aswclear.exe (download from avast.com) run in safe mode between the two).