If you don't have some applicable insurance (e.g. collision), the only way to seek compensation is to sue. You can either sue using a fictitious name (e.g. "John Doe #1, owner of the black cow which destroyed plaintiff's car") and then subpoena the farmer who says he knows, to force him to testify and tell you whose cow it is; or you can sue that farmer, and he'll be forced to identify the person it was to get out of the case (and you can also again use subpoenas or other mechanisms of "discovery"--e.g. written questions, called interrogatories--to find out what he knows). Therefore, there are ways you can get this information, but they involve instituting a law suit so you have access to legal process. Ideally, you should retain an attorney to help you, though you are allowed to represent yourself pro se (on your own; no lawyer).