If you are trying to telnet to those ports on the remote computer, those ports do not need to be open on your firewall. Open ports are generally for incoming session establishment, not outgoing sessions.
Web browsers use the HTTP protocol on TCP/IP, where ping uses the ICMP protocol on IP, so it is very possible that ICMP requests or replies will be blocked somewhere along the route, but web browsing would work without an issue.
If you are trying to see if ping will work for you, try "ping
because they do reply.
It appears that you are using Windows for your OS, but I am not sure which version. If it is XP or Vista, then it is possible that you have a software firewall on the PC itself (built-in, Norton, McAfee, etc.) that may well be dropping ICMP packets. I'd check that first. You may also have a router and/or firewall that could be affecting your ability to connect to this server (or application). And the other end could have a firewall and/or router that is blocking your incoming connection. But, since they are recommending alternative methods of connecting with them, it seems likely that their firewall/router configuration is designed to let you connect.
How were you testing ports 23, 3001, 3002, and 9021? Were you telnetting to them manually or using the web browser?
You may also want to install Wireshark on your system so that you can capture packets to/from your PC to help you troubleshoot the problem.
pansophic