If your close to the router you can still plug a Network Cable into the router "Hub".
Depending where you buy the cable it be about £1 per meter with the ends on moulded for durability.
Sorry that's way over the top.http://www.amazon.co.uk/Cat5e-RJ45-Ethernet-Network-Cable/dp/B000IAHNVG
35p for 5 meters they may be delivery on that but under a fiver. Your old pc will normally have a network card to accept this cable.
It may look like the same connection as a modem but its not.
This is a cat 5 cable with a rj45 connection.
Your modem was a telephone wire with a rj11 connection.
the rj45 is squarer if that's one way to say it.
They both have the nick in the top.
But the rj45 will not fit in the rj11 slot in the modem.
Its the net work card you will need with the connection.
You dont say what the operating system is for your computer so you must make sure if you buy on you have the one that will work on an old machine.
Hope that helps.
If you get stuck or want more help drop me a private message.