If it's still under warranty, call for repair. If it's not, you're in for either an expensive ($400+) mainboard replacement, or you can give a try with a shop that can solder in a new power jack (www.aqstech.com is one); charge for that should be about $150.

My Inspiron 8500 has given me a similar problem in recent months. Dell wanted over $500 for a MB and local repair shops wanted over $300. I finally took the gamble and bought a refurb MB on Ebay, installed it myself and all is well again. After I return my old MB it will end up costing me around $120. I've always been hesitant about buying electronics on Ebay but this vendor was very helpful and provided fast delivery with a 90 day warranty.