Is this on a Lunarpages server? We only permit discussion of LP hosting here.
If you're on a shared server, you do not start a MySQL server yourself -- support does it. They may not be aware that it's down, and you would need to open a support ticket to let them know. If this is a dedicated or VPS/cloud server, I'm not sure what the protocol is, but you should already have sufficient access to take care of such things.
If starting the MySQL server is not what you're asking for, could you clarify what you're trying to do? If you actually need to start something running, telnet or SSH is not the only way. Even on a shared server, you can use the control panel to run a one-time "cron" job that runs a command (be sure to remove the cron job afterwards, so it doesn't run again).