[strike]So the ones that say ethernet will look like phone jacks but a little bit different, this is RJ45.
However what you are wanting to do is frankly rare as rocking horse doings, so there are some if's and buts to work through. Modern RJ45 connections should cope with a pc to pc connection with a normal network cable, they should autosense that this is what is happening and not need a special network cable. However your's might be an oldish device, so you might need a cross-over cable. BUT given that it is 4 port it might have a switch built in, and therefore need a normal cable.
So try a normal network cable, and if that doesn't work get a cross over cable.
At the laptop end you just need a network port, which most non-ultrabooks will have as they are not too slim.
Now your PC would need to on whilst using the laptop. [/strike]
ignore all of that, no idea why, but I thought your modem was a card inside your PC, and not a separate device, in which case you have a perfectly normal and follow what snipergod says.