First search for a long unique sentence of text from the page. If it finds it, it isn't removed, so you're half lucky. Then look to see what comes up first under that string.
Just a short time ago we had a case where the exact same thing happened. We had a domain in the top ten for years, then one day a couple years back it vanished. It was consistently top ten on Google, alltheweb, etc. and most of the other sites who came up in the top ten on them were there on the PaidInc too whether they paid or not, but our site was always mysteriously missing from the ordering. We even submitted the page via paid inclusion and EVEN after that the only way you could still find it was by typing in the full domain name (including the www!) We wrote, called, complained to incompetent Netsol folks (who we submitted the paid inclusion through) and to ignorant inktomi doofusses (I had a more descriptive word in mind but it would have gotten this posting cut) and they all insisted it WAS indexed, GUARANTEED it was NOT penalized or blacklisted (I still have the e-mails archived) and then they'd cut and paste the typical legally constructed statement about not guaranteeing WHERE it would rank, yada, yada. This went on, literally, for years!
It was not until I started experimenting on my own by typing in various full sentences from the page to try to get it to come up SOMEHOW other than via the domain name, that I suddenly discovered the reason. Turns out SOMEHOW, they once-upon-a-time indexed a mirror copy of our home page from 1999! Someone (on our own staff unfortunately - back when search engines didn't seem to notice duplicate pages as much) had put a copy of our home page into a subdirectory on another related domain, which we had totally forgotten about and no longer maintained, but which somehow Inktomi had found and spidered long ago (maybe as long ago as when they actually accepted free submissions.) There had not even been any links to it in years, and our real home page had changed by about 60%, but they still kept it in their index. This 60% was enough to apparently get us a duplication penalty. I guess they assumed the old one was the official copy because it was older (the official page had been updated frequently.) Of course the lack of ANY links to the page meant it ranked below, ground level.
We immediately deleted and 301 redirected the copy page to our real home page. It took a while (up to months on some engines) to propogate, but after so many years, like magic, we finally returned to our rightful ranking among our competitors on the other engines. There may have been a faster way than waiting for re-indexing, but after dealing with the bozos previously we figured it best to just avoid any communication with the nincompoops altogether.
Now, what does this show about how your competition could easily destroy you? Since these particular search engines are such idiots and won't own up to their own mistakes, I'll make the solution simple. If one were so inclined your competition could copy your home page to an obscure location where they have no other outside links to it, spend a few bucks to submit it to ink and fast, then wait for you to modify your home page, so your is newer. As long as you don't make TOO big of changes, the same thing will likely happen to you as did to us.
NOW, maybe if the search engine people are out there reading this they'll fix their stupid mistakes and stop lying to paying customers, before it wipes out their credibility altogether.