I did not have a T series keyboard to rip apart but I do have one from a 600 series. I removed the space bar key and took a picture of what I believe you are describing:
http://www.rkawakami.net/ibm_600x/images/space_key.jpg
Is this what you are talking about? It appears that the key button is (most likely) a dome with a conductive elastomer inside the top surface. I am not aware of this being available to purchase from any laptop parts source. It
may be possible to re-glue the button back onto the keyboard, however you must be careful not to contaminate the disc over which this button is placed. If you are able to repair your key in this manner, please post your results here. I'm sure others could benefit from this procedure.
And if you cannot get the rubber cap to work again, then I'm afraid my previous advice still applies: it's probably not worth the effort to take the entire keyboard apart in an attempt to fix this one key (assuming you can get the part which needs replacement) when complete keyboards can be had for about $15-$20 on eBay.
(edit: BTW, there are a couple of diagnostic programs which can test your keys. I would recommend PC Doctor as it is provided by IBM for the T2x series on their web site.)
(edit2: OUCH! What a pain it was to get those four plastic 'arms' in just the right position so that the space key could snap back on! I learned that the trick is to get them interleaved with the pins inside the matching holes and then slide the key back on, aligned over the plastic arms and then firmly push the space key down until it clicks.)