Meaning of 始まりやした?

In this case, it's a more emphatic way to say 始まった. The pattern it follows is verb stem + は/や + する/しない. や is more colloquial... or perhaps it's more of a regional difference, I'm not sure.

Unlike 始まりました, 始まりやした isn't in the polite ます form. It does sound rather familiar, but the やした part comes from は+した, not ました.

You can find some examples of it on Weblio, particularly for やしない. As you can see, it can also follow the stem of potential verbs as well, to make phrases like "飲めやしない" (I can't drink [this] at all) and "眠れやしない" (I can't sleep at all). It can even be affixed to する itself, as in しやしない.

If written as はしない, as in "結婚しはしない", は is read as "wa", because this is the particle は.

It's also fairly common in the phrase "と言ったらありはしない" and it's derivative, ったらありゃしない, meaning, liberally translated, "to the greatest extent", or "nothing is more~". 勿体無いったらありゃしない means, "It's such a terrible waste".

/r/LearnJapanese Thread