I'm so sorry. I hope the mother didn't produce lethal guinea pig pups, or they may all end up like that
Was this one white? Are the others? Did you buy from a pet store? If so, you could expect to buy 'lethal' pups. A lethal guinea pig is produced by breeding roans or dalmations to each other, and can die early, come out blind or deformed. Otherwise, if they came from a pet store that one could have been ill. If they did or not, see the vet to chck the other piggies for illness. Some are catching and you need to completely sort out the cage.
I know you may not want to think about the old one now, but it's important for the survival of the other ones.
To answer your question about introcuding a new piggie, it should be ok, after your other ones have been in quarantine for a few weeks. Of course, you should purchase the newbie from a good breeder NOT a petstore, or adopt from a rescue. When the new one comes home, you should give him/her a day to settle in and then follow the steps of introducing which is on the last paragraph of this page: www.guineatastic.com/introducingfighting.htm .Are you completely sure of the gender of them? Again if they were recieved from a pet store, they could be anything other than they tell you. Have a look online for great photos http://cavyspirit.com/sexing.htm this website is great and shows how to tell young week old pups apart. You may want vet confirmation too to ensure no pregnancies occur.