I inherited an old Compaq 1275 notebook, (has only 4 GB of total hard drive space) and I'd like to see if it's capable of a wireless connection to the internet through my own connection on my newer HP notebook. Is it capable with some sort of wireless adapter card or something for me to purchase? What's it called?

As long as it has the slot for a notebook card, you can get a wireless card for around $30.

I agree with pro, but you might have trouble finding a card in the old PCMCIA format. You may have to go online for it.