Scanning slides

It's a dull dreich day here and snowing again slightly so I'm going to try to digitise some 35mm slides (we've got 1000s of them). I say 'try' because my laptop computer keeps telling me that I need more memory to get the resolution I want/need, and so far 2400dpi is the best I can get. This is barely acceptable and the images are huge - typically 20MB!

Thing is, I'm not even sure that using a flatbed scanner, which claims to be able to give a resolution of 4800dpi, will actually give decent quality images even if I buy a new computer with more memory. I've currently got 2GB. Opinions vary and a proper film scanner, it's suggested, is the only way to get really good results - or get them professionally done at the price of a decent house!

Anyone got any experience of this? Thanks.