If I'm on a Windows 7 or for example on a standard Ubuntu machine and I want to check if a server is up, what are alternatives to ping? If ping is disabled and does not answer, what can I then use?
You also can use telnet with the proper port (if you know which service is serving by this server)
if the server is yours and is invisible from internet, you can create automated script on the server to put a file with timestamp somewhere on public ftp server from time to time and check that file.
If the server is invisible from internet and you own a visible web server somewhere, you can create automated script on the server to get some page (even non existing one) from the web server and monitor web server's log files for the pattern.
Maybe you could use a port scanner, so if a port is open (for example netbios, http or anything else) you will get reply and know that machine is alive.
Or if you know username or password, can use SNMP or WMI and try to get information about machine.