Thank you so much for playing and the review. I like your thinking on how to solve the puzzles. :)
You were right about the Rembrandt date being the code. Did you press enter after putting it in?
Here are the codes for all three rooms for you and maybe for someone else who is also stuck:
Room 1: Date of the Rembrandt painting i.e. 1654
Room 2: The clue is 2143 and you have to enter the number of corners of each of the paintings in the correct order. The first painting has 4, second has 0, third has 2 and fourth has 6, so the code is 0462
Room 3: Use the corresponding number of each of the alphabets, so E is 5 and I is 9. Add for X and T so X is 2+4=6 and T is 2+0=2, so the code is 5692