The existing answers only seem to partially address the problem. (Disclaimer: this is my understanding based on somewhat rusty recollection; it's been a while since I watched either the movie or the show.)
As noted, there are a LOT of possible addresses. The chances of finding a working gate dialing randomly are slim. A fair bit was said throughout the course of the show with respect to the need to find valid addresses; in particular, most of the addresses they had came from somewhere (I forget where), but only the Abydos address worked without drift compensation. Once they learned how to compensate for drift, they were able to get other, known addresses to work. Dialing randomly, however, was unlikely to establish a connection. Unlikely, but not impossible.
Another potential problem is just how the gates actually perform addressing. DHDs were said to have some ability to compensate for stellar drift. This may or may not correspond to translation of the symbols into other symbols, or to somehow directing the gate itself to make adjustments.
Heliopolis was a random dialing. It worked "by accident", and the address they dialed may or may not correspond to the "proper" address. If the drift correction worked by translating a known address into the appropriate symbols for a gate's current location, then obviously no "old" address would work, because they are wrong. If it works by altering the gate's targeting, then only (known) addresses whose gate was "close enough" to unchanged would work.
In either case, however, Heliopolis was a case of simply stumbling upon an address that worked... and note particularly that in both cases, the address that was actually dialed would not match the "proper" address for Heliopolis, had it been known.
In theory, we might be able to tell by comparing original dialing sequence circa 1945 to the "present day" sequence. If they're different, that would suggest that the correction happens in the gate itself, and (knowing now how to do it) the team back-computed the original, "proper" address for Heliopolis. If they're the same, however, it's inconclusive, because they might have just disabled the correction to dial Heliopolis. A more conclusive test would be if we ever see a "known" address appear somewhere outside a dialing sequence, and a different address dialed on the Earth gate for that same destination.