Macbook novice - crash during software update, now unable to open software - HELP!

Hi there,

The power connection to my Macbook was pulled out during a software update and it lost power. I can log in and connect to the internet still, but every time I try to open an application I get an error message saying that "X cannot be opened because of a problem. Check with the developer to make sure X works with this version of Mac OS X. You may need to reinstall the application. Be sure to install any of the updates for the application and Mac OS X".

I've tried re-running the software update, but get an error message saying "Software Update quit unexpectedly."

Is there anything I can do to correct the problem?

Any advice would be enormously appreciated!

Thanks.