Well, you should not care about "computer is Started" if you are going to check "Application is Now ON" ;)
There are three main ways: first send broadcast and receive answers, second - keep list of "buddies" and check each one personally and third - connect to dedicated server and ask about clients (each client should report to server about status of couse).
There are some more, but they are not as intresting. Example: each client should send broadcast every say minute and everybody should receive such brodcasts and note "ok, he is online one minute more".