If the battery is in such a state, any under volt that the components receive (if any) shouldn't affect the anything. What you would worry about, especially with a laptop is an over volt, which in turn can cause a major league short. One worry though are the sudden shut downs/power cuts. Some components like hard drives do not fair so well with such issues. On a side note, how old is the battery/notebook? If it is under a year or if you have a warranty, call HP support and get another for free. If not, you'll probably want to save up and buy one eventually, especially if you use it off line a lot.