The short answer is NO, unless you have iWeb installed on that Mac and you also have your domain.sites files, which are your iWeb files that are found under your User Library/Application Support/iWeb/domain.sites.
You can install iWeb on that Mac by using the install disc for your old MacBookPro if you have it and loading iWeb onto it. You also need to have your iWeb data files where iWeb saved all work, which are your domain.sites files as described above.
Unless you have both of these on your current Mac, then there is nothing you can do to edit the sites with iWeb - you need to have iWeb installed and also your domain.sites files to be able to do anything in iWeb.
You can however download the html files from your sever and you can make alterations directly to the html, by using an html editor such as TextWrangler, but not using iWeb, as iWeb has no import facility, so cannot open html files.
Either that or you can use another programme to edit the site, but it has to be one that has an import facility, such as DreamWeaver or Flux V. Both of these can import html.
Other than that, you will need to start re-building your sites in another app that is supported, so I would suggest that you take a look at something like EverWeb or Freeway Pro/Express and others that are current applications.
