I understand it, but more direct, clear way of saying that is: 時計が止まって時間が分からなくなった。(the clock stopped so I can't tell what time it is)
様 is kind of a convenient word to convey "appearance" or "look"
時計が止まって時間が分からない様になった。(the clock stopped so that it's at a state that you can't read the time)
時計が止まって時間が分からなくなった。(the clock stopped so I can't tell what time it is)
Small differences but does convey similar message.
Maybe a similar comparison in English is, "it looks like xxx" and "it is xxx" (e.g., it looks burnt, it is burnt)