Easiest option if not needed to be portable use a external USB keyboard. I've seen one locally that sells for $29 that is slightly larger than the laptop keyboard it uses as a keyboard that would be portable if the laptop need to be moved around
All the connectors are designed to press down the cable to ensure a connection and that is why just pushing it into the connector will not work.
The type that slides in and out is what I have tried this on and on that one it worked. Someone else had tried to fix it and lost the slide piece. I was able to slice up a business card to the width of the cable and use several layers to get a secure connection and then tape to hold the pieces in place. That one is still in use.
Please note that I have never tried this on the flip up type as shown in your pictures. If there is room to push something stiff in above the cable gently as you do not want to break the white part. See if it works then. If so tape it and be done. Use a good grade of tape that won't dry out and shift around inside the laptop. If it goes in easy try a second piece between the cable and the top of the white connector. Repeat if necessary.
Glass tape, the one with fiberglass fibers in it is pretty durable.
If the cable does not go in far enough then several options depending on your risk factor.
shows some inexpensive motherboards under $100 if you feel safe buying on ebay.
Desperation type repairs below and I would only try them if I had to make it look original and I was prepared to order a motherboard if they went wrong.
attach something to the white connector with Crazy Glue to make the slot deeper and try again or, a lite touch with minimal expanding foam keeping in mind that if the foam gets under the cable then big problem.
Edited by rotor123, 14 December 2011 - 11:46 AM.