One alternative method to the tape trick that worked for me goes as follows:

0. To prevent possible damage, please do everything listed very gently.
1. First, slide one of the corners of the cable into the socket. If the corner is properly fitted, the cable shouldn't go up when you stop holding it down with your hand.
2. Next, slide the corner to its corresponding side (eg: if you slid the right corner, then push it to right). This should leave you with one side of the cable more tucked in than the other; but the whole cable is now in the socket.
3. Gently, try to push the cable the whole way in. At this point it's trial and error, but it's faster than trying to slide the whole cable at once in my experience.

If the cable is correctly inserted, the white lines on it should all be "connected" or under the black top part of the socket.

When reinstalling the cable, it is quite easier to do WITHOUT the display data cable retainer (step 17), in case you are reassembling everything in reverse order, as said in the guide's conclusion.

While this can make the resitting of the cable easier, one of the retainer's screws is directly below the cable, so you'll probably have to do some funny screwing to reinstall the retainer.