computer monitor will not start back up.

Whenever I get on my computer and i shut it off and i try to get back on it the monitor (an LCD monitor) says that it can’t connect to the computer. However when I wait about an Hour and I turn it back on it connects. What is the deal with that? it really bothers me for i can not restart my computer for a windows update or anything… Does anyone have a solution? thanks

The message actually says:
self diagnostis:
No signal
check connections

also, When I restart the computer it has about a 2 second long beep and then this message is displayed

Thanks,
Alex