Learn Turkish: Nankör adam hiçbir şeyin kıymetini bilmiyordu. - The ungrateful man was not appreciating the value of anything.

In Turkish, the phrase kıymet bilmek (literally "to know the value") is an idiom that means "to appreciate" or "to value" something. So, kıymetini bilmiyordu translates naturally to "was not appreciating its value" rather than literally "was not knowing."

Can you break down the suffixes in şeyin kıymetini?

This is a genitive-possessive chain that is also receiving the accusative case. Hiçbir şey-in ("of anything") is the genitive part. Kıymet-i ("its value") is the possessive part. Because this entire phrase is the direct specific object of the verb bilmiyordu, we add the accusative case marker -i using the buffer letter n, resulting in kıymetini.

Since hiçbir şey already means "nothing," why is the verb bilmiyordu also negative?

Turkish requires negative concord (double negatives). When you use negative-polarity words like hiçbir (any/no), hiç kimse (nobody), or asla (never), the verb must always take a negative suffix. So to say "he appreciated nothing," Turkish logic dictates you say "he did not appreciate nothing."

Could I use the simple past bilmedi instead of the past continuous bilmiyordu here?