The IP number you're going to enter is just a number to identify your machine on the network at the IP level (don't get too concerned with that). Everyone on the internet has an IP number. There are certain ranges of numbers which are not used on the internet and are set aside to be used locally, to avoid confusion.
Usually these addresses start with 192.168.X.X where X is a number in the range 0-255. The mask that WTT suggested of 255.255.255.0 is a little more complicated to explain, but trivially it means that the other computers on your local network must have the same first 3 sets of numbers and a different fourth number.
Now, the reason your machine isn't booting quickly anymore is most likely because it is trying to automatically get an IP number from somewhere. I would expect this only to happen if the cable were actually connected to the card, but I could be wrong. Operating systems will try and automatically get an IP address from a DHCP server (something else you don't really need to be concerned about). Your broadband provided, or a small broadband router, will contain a DHCP server, and will give you an IP address when you get your modem or a router (depending on whether you're just getting broadband, or whether you're setting up a network like you mentioned).
By setting a "Static IP", as suggested by WTT, you will stop your computer from waiting for an automatic IP number, and it should make it boot like it used to. When you switch to a local network or your broadband service, you will most likely have to change the IP number you have set.
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