Did you install as a "service" or as a "user"? If as a "service" it should run any time the computer is on, if as a "user" it should do what you are describing as long as that user is not logged on.
Do a search on installing Boinc as a service in the messages and you will find the exact process.

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I install boinc, the latest version, on a 2400+ AMD, with Win XP SP2 fully updated. It runs fine, with no problems, just like on my other very similar computer, until I reboot. Once I reboot, it turns on at startup, then turns off (disappears from the system tray). If I turn it on, it turns on for 1 sec, then turns off. The graphics show up, and if I leave them on, it works until they are turned off. However, it doesn't send the results cause Boinc isn't ON. My 2 computers are almost identical(same OS and software), the only difference being blackice firewall, but I turned it off. I'm at a lose.

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