I work in IT and worked for a major computer manufacturer on their level 2 helpdesk for 4 years as well. Yes, leaving the laptop on the charger with the battery at 100% is going to hurt the battery over the long run. So does not letting it drain fully before charging it. Extreme heat and cold effects batteries as well.
Almost all the major manufacturers like HP, Dell, and others have a one year limited warranty on their battery. Most of the batteries with care can last 2-3 years but I have seen many many batteries fail just after the one year warranty. All the batteries for HP, Dell, Etc. are purchased from the same manufacturer's overseas so this is pretty common.
Bottom line if your laptop battery is not powering the laptop by itself for more than 30 minutes you probably want to go ahead and replace that battery, but check and see if its under warranty first. That is the standard by which Brand X replaces most of their batteries.
Your friendly computer guy!