I just installed ubuntu 10.10 on a five year old
Dell Inspiron 1000. The computer works great and boots fast. I cannot get the
Dell wireless 1350 PC card to work with wireless. Internet works fine with
ethernet connection. Any help will be appreciated.

Have you enabled the restricted packages in Synaptic Package Manager ?
These add in a lot of support for things like wireless card drivers
and it may be all you need to do so worth a shot

Broadcom chipset wireless and ethernet used to be a real pain to get
going in Ubuntu ( or any other Linux ) but recently there's been a big
improvement in the support for these.

Open Accessories/Terminal and enter the command:
lspci

One of the lines will look like this:
03:07.0 Ethernet controller: Atheros Communications Inc. AR2413 802.11bg NIC
(rev 01)

Where "802.11" identifies the line. Then take the model code, which is "AR2413"
in my case, and feed it into Google. I would also try including the words
ubuntuforums and solved, and perhaps you will get lucky.