Before you buy a new computer, think about whether it could be the battery instead. Laptop batteries are not manufactured for eternal recharging. You might think you’re doing the right thing by keeping it plugged into a wall charger all of the time, but you’re actually doing your battery a favor by unplugging it every once in a while.
One other suggestion: don’t let the computer get below 20% charge before plugging it back in. This can help preserve battery life.