you do not need a second modem.
If you were to use that 2nd modem you would have to end up paying more.
What you need is a router.
This is used to share broadband connections on more than one PC.
Your cable modem connects to the router and then all computers you want to have net access connect to the router.
The router takes care of internet sharing and handling the connections.
This allows everyone to use the internet at the same time on all PC's.
You can either buy wired routers for about £40 where each PC connects by wire or wireless ones that cost a bit more where you can have PC's in different rooms in your house and they connect wirelesly thruogh the air.
You just need ethernet cards in each PC and hook them up via CAT5 cable to the router.
You can buy kits that are ready made for you with the ethernet cards and router and cabling if thats better for you, but I assume you have ethernet cards in your system already.
Look at Linkysys routers. They are good.
eg., This one which is quite cheap and quality:
Linksys Router
Or a wireless one
here
(If you go wireless you'l need wireless network cards in each machine too.)