I am sorry for not answering sooner, but was watching our Seahawks win the Super Bowl. I live in Eastern Washington state and have been a Hawk fan since their beginning, through thick and thin.
Yes, it certainly looks like you have some bad capacitors. It's to bad, but the least expensive HP computer will be light-years ahead of your old one. If you decide to buy a new computer, I will be glad to help you get the biggest bang for your buck. All I need to know is what you do with a computer.