|Laptop no video (or video problems), and battery, AC adapter, power jack T shooting.|
See response 1:
Laptop main batteries usually work as they should for a year or so, then they begin to rapidly deteriorate. From what I've seen, by two years they cannot be charged to anywhere near their full capacity, and it gets worse after that.
They often develop internal shorts when they are older. If the battery gets HOT rather than just warm after you have attempted to charge it for at least a half hour, or after you have been using the laptop for a while with the AC adapter plugged in, it's definitely internally shorted and you must replace it. Internally shorted batteries getting too hot have been known to cause the laptop to catch on fire.
Tips about battery charging problems on Dell laptops - may apply to other makes.
See response 3 in this by iTech: