i think the OP could do something close to what he wanted with an hta file. essentially this would be a web application that was *installed* client side but still interacted with a remote server. an hta file is designed like any other javascript + html app but is run from the client-side. it has wide privileges on the system and so can fire off local programs and other scripts without an issue. similarly toolbars and other browser helpers can do the same thing. the wide privileges can also be used to update itself so, apart from the initial pain of downloading the starter app, the experience is the same as a web application. the server calls would typically be made with xmlhttprequest.
i don't know of the cross platform abilities of an hta file - i suspect, since they're more or less locked to internet explorer, cross-platform is not in the vocab: which may make a toolbar/helper approach more palatable if your design constraints include multi-platform/multi-broowser.
additionally php provides a GTK which again can be installed locally and interact remotely. i've never tried creating a client-side php app - i'd be interested to hear from anyone who has and what their feelings were about the GTK.
alternatively again ... an ajax intermediator like DeskRun might be what you are looking for.
and lastly (as a suggestion) you could develop entirely server side and use a framework like dojo to manage offline (client-side) data storage with dojo.storage. The learning curve into dojo is steep but if you just want to make use of single features then it's no more than an hour or so. I'm currently working on an easy way to detect online status and synchronise offline stored database edits (for example) with a server. Apart from getting the business rules right, the technical side is trivial - it's finding the time that's a problem!