First of all, if it says in your contract that you can't run servers, doing so may result in your connection being cut, so do this on your own risk! Second of all, I don't advocate running websites on a home machine. Get a VPS!
All this said, if you do run a webserver on a home machine and want to make sure that your ISP isn't blocking it, here are some ideas on how to test it:
- Use TOR to browse to it
- Use a free proxy to browse to it
- You could have used the Google translate trick, however they closed this loophole.
- However you can still use other services like ViewHTML or even the W3C validator to test connectivity.
As for other services (SSH, RDP, etc) - you could use something like nmap online to scan your host and determine if it sees the given ports as open.