I've seen на́чался, начался́, and нача́лся listed as past forms of this verb. However, there's no explanation as to when one form is used over another. Is it a matter of register? Are some of the forms preferred over others in literary style vs. conversation? Is there a particular meaning associated with any one form?
Some works exploring stress variability in Russian show sufficient difference between the declared standards and real language spoken by educated natives. E. Markland Sharapova (2000) tested 106 speakers in Moscow and found out that most of them considered it unnatural the 'standard' stress on -ся in начался́ / заперся́ / обнялся́. This conclusion might change my previous opinion: I used to think that the version на́чался was more typical for St. Petersburg (the words пока не на́чался джаз from a song by a local musician Grebenschikov never sounded strange to me), than for Moscow. The normative version начался́ sounds a bit formal to me, expectable to hear it in some news by a central TV channel, or maybe I'd even use it myself when speaking about the beginning of a concert, as opposed to the case of a sudden rain.
A page from the book Акцент и ударение в русском языке by Вернер Лефельдт, where E. Markland Sharapova's work is quoted:
Russian doesn't care about stresses as much as, for example, Chinese.
There are obvious cases where putting a stress on another syllable would make the whole word sound really wrong (
лЮбовь as an example). If you put your stress in the wrong part of the word you would either sound weird, or won't be understood at all.
In other cases while the form might not be in a dictionary, it's still valid as a vernacular, though using it will indicate that maybe you're not too educated.
На́чался is that case here. A person might use non-dictionaried versions with some slightly different tonal meaning, but I won't be able to provide an example, so subtle that will be. It won't affect your understanding, and you would be quite right to stick to the dictionary.
Then there are cases where even a reasonably educated person doesn't know how a word should be accentuated, a common example is
тортЫ. The right one, according to dictionaries, is
тОрты, but you are likely to hear both variants equally, and most people won't blink on either. Only people that have particulary strong feelings about "right" ways of speaking would care if you don't use the dictionary form.
And, as an edge case there are heteronyms, there aren't a lot of widely used ones, but
замОк (lock) and
зАмок(castle) are among the most common examples. You should know the difference with them and just you what you need to. In writing, the meaning is derived from context, just as with English examples (dEsert as area vs. desErt as an army desertion).
I'm not sure of an example, but those cases might mix and match - some stresses would be wholly invalid, while others would simply be less accurate