battery issue

If its under 12 months old then you are covered by warranty

Do a SMC Reset

http://support.apple.com/kb/HT3964

Additional Information

The System Management Controller (SMC) is responsible for many low-level functions on Intel-based Macs. These functions include:

• Responding to presses of the power button
• Responding to the display lid opening and closing on portable Macs
• Battery management
• Thermal management
• The SMS (Sudden Motion Sensor)
• Ambient light sensing
• Keyboard backlighting
• Status Indicator Light (SIL) management
• Battery status indicator lights
• Selecting an external (instead of internal) video source for some iMac displays

Other threads here

https://discussions.apple.com/thread/4072540?start=0&tstart=0

your mac's battery may have been hurt by misusing it, the battery is not ment to stay at 100% or 0% charge for extended time. If you leave it on charge during a trip for 2-3 days regularly, your battery may become damaged. the best charge to leave it on is around 50%, also depending on how old the battery is, it may have reached its maximum life time. also try not leaving it on power all the time even when using, and fully run down you battery to 0% then back all the way to 100% again right away. you can do this about once a month for best results. you battery at this point may not be saveable but with these you may be able to get a little more out of it.

also see

http://support.apple.com/kb/TS1909