@shinnen I am sure you have already double checked to make sure that you have a memory stick that is meant for your camera. The wrong stick can give you issues like this as well.
Since it seems to have mechanical issues (if you are 100% sure you have the right memory stick) as well, it appears as if the issue here is caused by your memory slot. It's time to disassemble your camera and to have a look at the connector etc.
To work on your camera you can get the service manual under the Document tab on this page [[Topic:Sony Cybershot DSC-T100]]
If you find anything "odd" or have a question about any particular step etc, you can always post images of that with your Question. Use this guide [guide|21499] for that.