If you reinstall on the same laptop then you don't use your install
quota given in the EULA.
I take it you are using retail version of Microsoft Office 2003. If
this is the case the you are allowed two separate/different
installations but installaing on the same laptop is still the same
installation.
If at the time of installation you have spent 120 days since last
activation, then online activation will be possible. If it is less than
120 days then you will need a telephone method to activate your product.
I always recommend people to activate online first as sometimes it just
does it even if it is less than 120 days.
hth