I need a software that would let me search files on my file server from other computers on the local network. My file server runs OpenSolaris. Preferably something that would offer the search via web page.
Have a look at Lucene. It's an open-source search engine. It does not do crawling etc. on its own, but there are many projects based on it which offer the capability.
Solr would be one project built on Lucene which might be what you need:
Apache Solr is an open source enterprise search server based on the Apache Lucene Java search library, with XML/HTTP and JSON APIs, hit highlighting, faceted search, caching, replication, and a web administration interface. It runs in a Java servlet container such as Tomcat.
The hackish thing to do would be to plug together Apache + CGI + perl|ksh + find + grep