My friend just bought a a 10.8v battery for her toshiba satellite that previously used a 14v battery I just need to know if there will be any problems if she uses her new battery.
Generally it's a "bad" idea to use anything that isn't a perfect match in terms of voltage.
Over-voltage may damage components (permanently) and should be avoided.
Under-voltage may cause components to be unable to function (but is unlikely to cause permanent damage); it might not work at all, it might work unreliably, it might work fine.
In this case, we're looking at under-voltage - which, as said, might work but I'd personally still recommend against it. And don't forget that the amperage and/or power output of the batteries should be compared as well, it's also important.
If your friend insists on using a weaker battery, I'd advice they turn down all the power settings to the lowest options they can stand.
Generally a bad idea if they're that much different. I'm surprised that it would fit. Usually the manufacturers go out of their way to make the cases different if the battery is incompatible with another one in their line. If new battery is not from Toshiba I'd be even more wary.