I would suggest not wasting your time and money on upgrading a 16 year old pc. Although I suspect this as more of a project since it doesn't make sense otherwise. There are other cheaper pcs that could be tinkered with.
As with any laptop cpu upgrade, it's going to be google, or trial and error. They don't release cpu support lists for laptops, not to mention gateway has no support whatsoever for old products. They don't even mention them like they don't exist. Besides that, pc parts typically only drop so low so you can buy newer better parts for the same price. Or in some cases an entire new pc that's better for the same price.