Many laptops have two "CPU power" levels - full speed, when the mains lead is connected, and "economy" when it's not. If you don't notice any difference, then worry not. My laptop runs at 1600 meg on mains, and about 600 meg (varying with demand) on battery.
Most modern(ish) computer batteries have a finite lifespan, based more on when they were made than how much use they've had. It was different in the olden days of NiCd batteries, which needed to be fully discharged before recharging. Modern ones aren't so fussy.
I've had to buy a new battery for most of my portable stuff around 4 -5 years old. How much use and how many charge cycles didn't make a lot of difference (some but not enough to notice). The laptop battery goes down slowly till it reaches 39%, then falls off a cliff to zero in about ten minutes.
Buying a replacement can be interesting - you don't want one that's been on a shelf for three years. Mine have a "manufactured date" on them.