My batter ran out while on vacation and I didn't get a chance to recharge. When I plug in the adapter, the batter icon on the monitor shows a black X. Can't seem to get the batter to charge, but the computer still runs when plugged in.

Anyone have any tips? I read something about a batter reset? Any help would be greatly appreciated!

Try looking up "deep discharge" in Wikipedia.

After that, follow these troubleshooting documents.

MacBook, MacBook Pro: Battery not recognized or "X" icon appears on menu bar
MacBook, MacBook Pro, MacBook Air: Battery not recognized after being fully drained

PS. Depending on the time when your battery stayed "discharged" there may be damage to the battery itself.

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iMac 20' Intel Core 2 duo 2.16GHz, 4GB DDR2-667 SDRAM, Mac OS X 10.5.1 "Leopard"
Hackintosh Q6600 4GB DDR2-667 SDRAM, 9800GT, Mac OS X 10.5.6 "Leopard" (EFI-X)
Macbook 13' Intel Core 2 duo 2.2GHz, 4GB DDR2-667 SDRAM, Mac OS X 10.5.6 "Leopard"
iPhone 2G (8GB) 2.2 (1.1.2 OTB) Week 48 J'B'ken + Activated + Unlocked

if it shows an X , then you're battery is dead. i own an iBook G4 and that happened. i bought a new battery.

Sorry for bad english, hope that helps.