If the question is “What reasonably well-known language which was spoken in 1007 A.D. and is spoken today has changed the least over that period?”, where describing a language as spoken means that it’s learned by children as their first language, then Icelandic is apparently the best answer. Classical Latin wouldn’t count, since it hasn’t been used as a first language by children for over 1500 years. Ancient Hebrew wouldn’t count either, since it hasn’t been used as a first language by children since about 200 A.D. (or possibly even earlier than that). Since the 1940’s, there’s a language called Modern Hebrew which is now learned by children as their first language in Israel, but that’s not the same thing as Ancient Hebrew. Modern Hebrew is slowly changing like any ordinary spoken language.
Classical Latin and Ancient Hebrew are examples of religious ritual languages, which are languages which are used by the clerics of religious groups to write and speak to each other, but which aren’t learned by children as their first language. They don’t change very much, since most of the processes of linguistic change are driven by child language learning. (They do tend to acquire new vocabulary for new things though.) Latin is the ritual language of the Catholic Church and Hebrew is the ritual language of Judaism. There are a few other such languages, including Sanskrit, which is the ritual language of Hinduism.
The claim is that Icelandic has changed surprisingly little since about 1300 A.D. I’m a little dubious about this claim, since in general languages change no matter what anyone wants. Language academies don’t actually have that much effect on the amount of linguistic change. L’Académie Française, for instance, has had less effect than it thinks it has on French. But, by most accounts, Icelandic has changed less than most languages do in a comparable period since about 1300 A.D.
Incidentally, the usual definition of the time periods of Old English, Middle English, and Modern English is that Old English lasted from about 500 A.D. to about 1100 A.D., Middle English from about 1100 A.D. to about 1500 A.D., and Modern English since 1500 A.D. These are arbitrary boundaries, of course, since English, like most languages, was always slowly changing. Incidentally, nobody uses the spelling “Olde English.” Most of the other languages which have written forms over the past thousand years or so are also split up, again somewhat arbitrarily, into periods of Old, Middle, and Modern (or some similar such terms).