Learn Icelandic: Hleðslutækið er bilað.

It is a compound word. It combines hleðslu- (from hleðsla, meaning "charging" or "loading") and tæki (meaning "device" or "tool"). The -ð at the very end is the attached word for "the," making it literally "the charging device."

The dictionary form for "broken" is bilaður. Why does it change to bilað here?

Adjectives in Icelandic have to match the gender of the noun they describe. Because tæki (device) is a neuter noun, the adjective drops the masculine -ur ending and takes the neuter form, becoming bilað.

Why is the definite article ("the") at the end of hleðslutækið just -ð instead of -ið?

The base noun tæki already ends in a vowel (i). When a neuter noun ends in a vowel, you just add -ð to mean "the" instead of the full -ið ending.