了 shows that the action you're talking about is completed. This could be already completed (in the past) or to be completed (like when you say "I'll go to the movies when I will have washed the dishes.")
以前 just means "before" or "previously". It marks past time. 了 does NOT have to mark past time.
Chinese has aspect (particles that show whether the verb action is completed, habitual, ongoing, etc.) instead of tense (endings showing when a verb's action occurs).