I was born to a Jewish mother. Yesterday I ate a dish which contained shellfish, pork and milk products. Do you exhort me to present myself before a Beth Din? What will likely happen if I do?
The first thing you have to understand is that nowdays, the Beth Din hs very little power, especially when it comes to distributing punishment. These days, Beth Dins deal almost exclusively with business issues, divorces, and conversions.
In addition, there is an important principle in Jewish law that a person cannot make himself into a 'rasha' (lit. evil-doer). What this means is that a person cannot testify negatively about themself. You can tell a Beth Din anything you like about yourself, but it won't count for anything.
In the past, when the Beth Din had power, and in the future, when it will have that power again, this is the procedure that would happen. You would have had to be observed eating your non-kosher food by two witnesses, (the criteria for witnesses to be valid are quite extensive) who would have had to warn you
immediately before you did the act that what you were about to do was against the Torah, and they would have had to warn you of the punishment you would receive for doing it. The witnesses would then go to Beth Din, whereupon their testimony would be examined extensively. If the Beth Din are satisfied with their testimony, you would receive 117 lashes (39 each for the pork, shellfish, and combined milk and meat).
I was born to a Jewish mother. Yesterday I ate a dish which contained shellfish, pork and milk products. Do you exhort me to present myself before a Beth Din? What will likely happen if I do?
Wouldn't that depend on whether you follow the religion or not? I think I read somewhere where you said you were an atheist.
Yes, I am an atheist. (Or whatever the correct term is for someone who tacitly renounces belief in a higher power.) However, I'd imagine that for orthodox Jews, if you're born a Jew you remain one, no matter what you do with your life. We'll see what Yitzl says anyway.
Anyone born to a Jewish mother is Jewish, no matter the level of observance. This is what makes being Jewish both an ethnic and religious matter.
Jewish != Judaism
Not true. One can be a Jewish christian, or a Jewish muslim, or a Jewish atheist. Being a Jew has nothing to do with what religion you are, it simply means you had a Jewish mother (or converted). Judaism is the religion which observant Jews believe that all Jews are commanded to follow.
*And as regards *this* community, surely you can name another Jew who doesn't expressly believe in God? 
Indeed, enwiabe is absolutely no less a Jew than I am.