In most cases it's just the one rolling-type bag, and then one briefcase or laptop or purse. See related link at the TSA website.
Yes, you can take a PC on a plane as carry-on luggage.
Yes, you can take your computer on a plane as carry-on luggage.
Yes, you can take DVDs in your carry-on luggage when flying on a plane.
Yes, you can take CDs in your carry-on luggage when flying on a plane.
Yes, you can take computers in your carry-on luggage when flying on a plane.
Yes, you can take a computer on a plane as part of your carry-on luggage.
Yes, you can take beef jerky on a plane in your carry-on luggage.
Yes, you can take DVDs on a plane in your carry-on luggage.
Yes, you are allowed to take an umbrella on a plane in your carry-on luggage.
Yes, you can take an electric razor on a plane in your carry-on luggage.
Yes, you can take an electric shaver on a plane in your carry-on luggage.
Yes, you can take a laptop charger on a plane in your carry-on luggage.