This is actually not the story of a Semitic root, but rather of an Indo-European one - and maybe two. But since this is Balashon, we will examine the root via Hebrew and Jewish words.
Answers.com defines a blech as:
A blech (from Yiddish) is a sheet of metal used by many observant Jews to cover stovetop burners on Shabbat (The Jewish Sabbath), as part of the precautions taken to avoid violating the halakhic prohibition against cooking on the Sabbath.
What is the origin of the term? In German, blech means "sheet metal". This site points out that the origin is the Indo-European root bhelg or bhleg, meaning “sparkle” or “shine" - I suppose because of the shiny nature of sheet metal. This root is the source of dozens of words including bleach, bleak, blind, blond, blank, blush, blue and even black (shine leads to burn, and burnt leads to black).
Another Hebrew word that comes from an Indo-European root is balagan. It entered Hebrew from Russian, and means a chaotic mess. According to this site, the etymology is as follows:
"balagan" is Hebrew/Yiddish/Polish "mess" - Russian/Turkic "wooden house" - Persian balakhaana "external room". But "balakhaana" can be derived from OIE (Old Indo-European) *bhelg which means "wooden plank". This ancient word's direct descendant in English is "bulk". And from this same root we have the Polish word "belka" (direct decendant) and the English "balk" (came via Old-Norse) - both have the meaning of "wooden beam", "girder", "tie-beam", "rafter" - (compare "fulcrum" which is a Latin relative to these two words).An even more interesting, the English word "balcony", Polish "balkon" (which came to both our languages from Old Italian (to Polish via French) where it came from Old Germanic, and which means "wooden platform", "scaffold". Although the word "balcony" does not come directly from the Parsian "balakhaana", but it is a similar type of derivative in another ancient language belonging to the same family, and nowadays it still keeps the similar sound and meaning.
So bhelg/bhleg can mean both "shine" and "plank or beam". Perhaps they are two separate roots that appear very similar. Or maybe burning wood leads to shine and glow? (This site - s.v. Fulginiae - maybe hints that it does.) Does anyone have any decisive information one way or another?