S.M.A.R.T. tripped

After a series of power failures during a stormy period, I began getting messages from Windows that there was a problem with my Hard Drive. Somewhere i read that this can happen if the disk is being written on during the failure, so I am hoping that it is not a mechanical problem. I attempted to fix it (reassigning bad sectors or something like that) using both the  Sea-Tools DOS and the Windows utilities but it didn't work. Somehow I think that the fact that S.MA.R.T.was tripped may have something to do with the inability to fix the problem.

Is there a way for me to fix this thing??

Also,if I install a new hard drive and clone the old disk unto the new one, will that fix the problem or will the ureadable sectors be cloned also??

I really don't know anything about computers so try to keep answers simple. I have backed up my disk by using both MOZY & the windows backup utility.

Thanks in advance.