thats quite an itneresting idea there, i wish I had the stuff to do it.
OK, Your laptop uses an LCD screen which is a digital display using the PAL standard. Your playstations video output is analog, NTSC(National Television System Committee) standard. Now, there is two ways two ways to do this, with out even looking i think converting the NTSC output from your playstation back to digital for your LCD screen would be easiest, even though it would be bulkier requiring room for the extra hardware. The other way would be to route the digital video data from the Playstation motherboard directly to the LCDs digital input bypassing the digital to analog converter used by the playstation. This method would result in better, faster, and cleaner video but there is a lot of unknowns with this method.
1 if the formats are even the same.
2 you need the pinouts both for the D/A converter and LCD so you know which wire to jump to where.
3 you could possibly need additional circuitry to control voltage levels
4 the electronic knowledge to do it.
if you can take a picture of the connector to your LCD screen or describe it. tell me the number of wires and all of the technical details you can. You can do a google search for NTSC to PAL converters see if you find anything to suit your needs, its really hard for me to say what your needs are and recomend something to you.
well I hope this gives you some ideas and understanding.