The laptop RAM (SODIMM 204 PIN) will definitely not work with that desktop motherboard.
I am not a super huge expert on keeping old hardware going long after its end of life, but I would say that if you find another RAM with much more similar specifications it will probably work.
240 pins is a minimum for it to have a chance of working.
This would be a decent tryhttp://www.newegg.com/Product/Product.aspx?Item=N82E16820134927
but I can't guarantee you anything unless you can find me a product page for the one you have now because I can't find one myself easily.