For the other issue, does the system correctly identify the AC adapter (f2 at powerup to check). If the adapter shows "unknown", you have a bad AC adapter, power jack or mainboard. A BIOS update will not solve this - replace parts in that order.
If the adapter IS recognized but the battery won't charge - particularly if the system is on its original battery, which is now 5-6 years old - it's time for a new battery. They do wear out over time -and anything beyond 3 years or so has had a good, long life.