Hiya Emma
It's not possible fr an egg to be fertilised by a dead sperm. Sperm have to be very much alive to reach the egg. Some sperms however, in the right enviroment (ie fertile cervical fluid) can live for up to 5 days. So in theory, you could have sex on a Monday and actually concieve on the Friday (assuming you are ovulating). A dead sperm would not even come close to reaching the egg as cervical fluid acts as a barrier to abnormal sperm, which are unable to swim in the fluid. This is natures way of ensuring that only healthy sperm make it through the cervix and uterus to the fallopian tube.
It actually takes the sperm quite some effort to penetrate the outer layer of the egg (cumulous oophoorous) - Only good quality, mobile sperm are able to do this.
Hope this helps