@Bren From what I’ve understood, you connect your laptop to an AC power outlet, and it charges sometimes, and does not charge at other times. I’d appreciate it if you could provide some additional details: 1. What method are you using to determine whether or not your laptop is charging? (Do you look at the power LED light which indicates when the laptop is connected to AC power?, or do you wait for Windows to start, and look at the power icon in the system tray?) Also, do you need to disconnect and re-connect the power cable for the laptop to start charging? Or does the laptop randomly start and stop charging when it is connected to power?
The two hour battery life seems normal. Over the years, batteries start becoming less effective at storing electricity, and for most normal batteries, once they’ve been discharged/recharged completely (known as a recharge cycle) about 200-300 times, they reduce to about 80% capacity. That’s not really anything to worry about, and is perfectly normal.
About the laptop getting hot at the bottom, yes- that could be dangerous, but not necessarily. It depends on how hot the laptop gets. Chances are that if the laptop’s working just fine and not crashing or hanging due to overheating, then it shouldn’t really be something to worry about. However, I don’t recommend ignoring the issue. Just a few days back, I ran into someone who had ignored his Mac Book Pro getting really hot from underneath, and it’s motherboard had burnt out over a few days. The guy had to have the motherboard replaced for almost 1200$. I’d suggest that you either have a professional look at the laptop, or you could use SpeedFan to monitor your CPU temperature. For most laptops, the temperature should be less than 70°C to be on the safe side, but that value could vary from processor to processor.
Download SpeedFan from http://www.filehippo.com/download_speedfan/
I hope that was of some help, and do let me know if the laptop’s really hot, so I can help you sort that as well.