The particular question I have is the following: Starting with three separate proteins, is there a bioinformatic tool which can be used to identify one or several molecular signaling pathway in which the function of these proteins converge?
Personally, there are loads of softwares available which can help out with enrichment analysis. Among the open-source softwares, DAVID, PANTHER, STRINGS SB, GeneTrail are popular softwares which scout data from KEGG Pathways, Reactome and NCI databases. Among paid softwares I feel Qiagen's Ingenuity Pathway Analysis (IPA), Thomson Reuters Metacore Gene Go are two very good softwares. I believe both there software have their own database which has an updated manual curation feature where researchers look for any new literature and its likely that you would get a really good output using GeneGo or IPA. Offlate I have been relying on Strings DB and FunRich for a lot of my analysis. I really like the visualization interface on FunRich. Many of the other freewares have a cytoscape plugin for better visualization.
So if your university has a licence for GeneGo then I would suggest that is something that I prefer the most. If you are looking at freewares then String DB and FunRich are two nice interfaces that I really like. You get a lot more info than just biochemical pathways using these tools.
In my opinion you should use different databases rather than enrichment tools such as DAVID where you have to input a list of proteins (more than three). I would start with UniProt information about GO and pathways and compare the information yourself to find matches. See if your proteins share domains, are regulated by a certain transcription factor, etc. At the same time you can also use text mining tools like Chilibot and GoPubmed and search for papers to see if they occurrences in the same publications. You can also use STRING as suggested before (input the three proteins gene names or accesison number) which will tell you if they interact or in general if they are functionally related based on coexpression, database search, text mining etc. You can also use GeneMANIA (input the three proteins) for the same purpose but also you can specify to add the 20 most related gene to those proteins and see if you can get to conclusions there based on shared partners.
Overall, there is not just one tool or tool type to do what you want just go over the ones I mentioned and see which of the help to answer your question.