|Well, lets tackle one issue at a time:|
The battery included with that laptop is most likely between 9 and 11 years old - it is completely worn out and the only way to get the laptop to operate without a charger is buy a new one, although new laptop batteries are generally quite expensive
This can be due to a variety of things, but the main cause is most likely the age of the laptop! If that laptop came out in the year 2000 then it is at least 11 years old now! Most computers now well over 10 times more powerful than those machines. Other than perhaps upgrading the ram the only real things you to try and speed up the laptop are
-remove all unneeded software
-ccleaner the hard disk
-perform a defrag
That should make sure that the computer is at least not running things it does not need to
This will be tricky to answer without more issues, but to sum it up to make sure that a virus is not the cause of the problem download a free antivirus (AVG and AVAST are both free and fairly good), make sure you have the latest definitions and perform a FULL system scan.
Other than a virus, the other main cause of the memory dumps caused by windows could either be due to overheating or malfunctioning hardware. When operating the laptop make sure that it is well ventilated, and that all of the fans are working efficiency. If the fans are not working properly it could be due to dust buildup - if this is the case you will need to open the laptop to clear dust from the fans/heat sink, if you don't feel confident enough most PC shops/repair places will probably find it no problem to help out.
Hope this advice helps!