Did you also use this after you defined the ACL:
http_access allow myhome Another suggestion if you cant get the no-ip to work, is perhaps defining an entire range of IP's. If you track your IP changes you should be able to work out a list of addresses. In my case I usually I only get a few addresses and they are all in the same networks.
Eg. I will get something like: 192.168.1.25 and then only the last 1 or 2 numbers change. So you could simply allow all IP's from 192.168.0.0. Not the nicest solution, I think your no-ip solution is much better if u can get that to work.
EDIT: Some info on how to enable more debug info to work out why you cant get access, In squid.conf enable debugging for section 33 at level 2. For example:
debug_options ALL,1 33,2 Restart squid then try and use your proxy, when it fails to work check the cache.log for the error. That should hopefully tell you why its not working.
Also just as a test to make sure your no-ip domain is working correctly as sometimes it takes a while for DNS to catch up, use:
nslookup no-ip-host-name That should return your IP address, check to make sure that is actually your IP. If they dont match its because the DNS servers configured are a bit slow to update. I found OpenDNS is pretty quick for updates. Let me know if you need more info.