That one is an odd one.
so both have wireless cards. The HP will pick up the signal fine, but the other will only pick up the signal if the HP laptop is on? And there are no hard wires between the two laptops, correct?
first thing i would do (and sure you already have) is get into the Toshiba's network settings and make sure everything is set up correctly. But even that would not explain why it is suddenly able to get a signal just by turning on the other system.