The quick answer is that there is no simple solution.
Online databases are a complicated issue by their very nature. In fact, most people run for the hills at the thought of a database for use on their desktop computer, never mind the added headaches of publishing one to the web.
Without knowing a bit more about what it is you want to do it is impossible to even begin to suggest possible solutions.
FileMaker is a good program but for web use most people plump for .jsp dynamic pages and this requires some pretty specific web hosting.
You say that the data will be static but needs to be searchable. There are CGI and PHP search scripts that can be used for keyword searches on web pages. A lot would depend on what you want to do with the data once a search has been run and a match found. If you want to display just the information that matched the search then you really are starting to lean towards a dynamic site.
Can you supply some more information about what the data is, or at least the number of data fields and what they are in terms of text, images or numbers ?
It would also help to know what your web host supports: ASP, PHP, MySQL, Access, MS SQL or whatever.
You don't convert data to ASP. ASP stands for Active Server Pages and, like PHP, the page is run on a web server, it performs whatever tasks and actions the programmer coded into it, then it sends the plain HTML output to the web browser that requested the page to begin with. The web browser never sees the ASP or PHP code, it only sees the HTML produced by the web server when it runs the ASP or PHP page.
Often ASP and PHP will interact with a database while beingh processed by the web server and may request information from it to display on the web page produced.
I'm afraid that without quite a lot of information to work on I'd be nuts to even try to suggest a workable solution.