What about the battery and screen?

Most likely the battery. If you're mechanical and brave you can disassemble and determine model number and replace. Unless if you've damaged/dropped it and suspect the screen is damaged. Batteries commonly only good for a few years - eventually they degrade. 5 years is common because of the charge/discharge cycles - where gaming units are commonly drained to almost empty before being recharged fully (best way for all batteries - short/low charge cycles wear them out faster)