I had bookings through other airlines on SQ flights. I have no problem seeing them in singaporeairlines.com.
Go to My Bookings.
Enter Booking Reference, last name, and first name.
Make sure that you have the booking reference for SQ system. For example, the booking code given by UA is only valid in UA system, and I will not be able to see it in SQ system for the corresponding SQ segments. After calling SQ to get the correct booking code for SQ system, now I can see the details itinerary including my seat assignment in the front cabin.
From previous experience, perhaps your computer need to be turned off and restart again.
For the two sites posted by bankops, SQ booking code will not work there. I can use checkmytrip.com to see my BD award redemption, and there it shows the booking code for SQ.