There is a variety of capture cards available, ranging from 20Euro to 2.000 Euro. You have to make a possibly hard choice, according to your requirements on capture: accepted resolution range, accepted frequency range, (hw/sw)compression, scaler functionality, reliability.
These cards operate together with some software specifically designed to capture the content (video/audio). Aside from commercial solutions (like AdobeFlashMediaLiveEncoder), there are non-comercial solutions, which require some manual hands-on to make them work according to wishes.
Here is an examplary setup of such a solution:
Though it might take some time to get the whole system running it might also show worth while. And, since this is a requirement, the presenter system is not modified.