If you want to know how long your specific laptop's battery will last go to the power setting in control panel and change the parameters so the display is bright and won't turn off and the hard drive won't turn off. This will somewhat simulate the battery under real use. Plug it in and leave it plugged on overnight. Then the next day boot it up and keep track of how long it goes until it dies.
You could borrow a battery from a friend and see if it charges their battery or buy another battery and see if it is charged by the AC adapter.
You should test the ac/dc power charger with a digital multi meter (DMM) and see if you have any DC voltage coming from the pack… if not replace.
If the AC charger works then my guess is that there is a faulty solder connection on the system board where the AC/DC power connector connects.
You can get a cheap DMM for $5 or less these days
MIT has developed a battery that will allow consumers to power up their laptop and it will stay powered up. The call it the ultracapacitor-a next generation super-battery. No comment was made when these will be commerically available or how much they would cost.
If there is too little amperage it could damage the laptop. It might cut off prematurely and possible corrupt the Operating System or possible cause damage to the hardware.
Your laptop will work fine as long as there are enough amps provided by the AC Adapter. So, if your laptop requires 4 amps and you use a 6 amp power supply you are cool.
The amperage rating of the AC Adapter tells how much current can be supplied, the laptop determines how much is actually drawn. You don't know you have all that power until you actually call on it. The voltage should be rated fairly close, but the amps don't matter as long is they are equal to or greater.
When you get your refurbished laptop it is very possible the battery does not work. It could be that it is just old and worn out or it is possible that the charging system on the AC adapter is not charging the battery. If you go to control panel and bring up power options you can see if the battery is being charged. You can also see if the battery light is on or turns green after it has been plugged in overnight.
To get the most out of your battery you need to know the type of battery and proper charging and storage procedures. If you buy a new battery they typically only a one year warranty and the battery can only be recharged 400 or 500 times. You can expect that it will last only two to three years. Prices for new batteries range from $50 to $125 or more. You can find good deals for used ones that will hold a charge for an hour or more on www.ebay.com for $25 to $50+.