My macbook's battery is fully charged, but the macbook won't stay turned on unless it is plugged in?

Battery Information:

Model Information:

Serial Number:

Manufacturer: DP

Device name: ASMB013

Pack Lot Code: 9a41

PCB Lot Code: 3f30

Firmware Version: ff14

Hardware Revision: 0011

Cell Revision: 00c8

Charge Information:

Charge remaining (mAh): 2456

Fully charged: No

Charging: No

Full charge capacity (mAh): 2536

Health Information:

Cycle count: 355

Condition: Replace Soon

Battery Installed: Yes

Amperage (mA): 0

Voltage (mV): 7713

System Power Settings:

AC Power:

System Sleep Timer (Minutes): 10

Disk Sleep Timer (Minutes): 10

Display Sleep Timer (Minutes): 10

Automatic Restart On Power Loss: No

Wake On AC Change: No

Wake On Clamshell Open: Yes

Wake On LAN: No

Current Power Source: Yes

Display Sleep Uses Dim: Yes

Battery Power:

System Sleep Timer (Minutes): 10

Disk Sleep Timer (Minutes): 10

Display Sleep Timer (Minutes): 2

Wake On AC Change: No

Wake On Clamshell Open: Yes

Display Sleep Uses Dim: Yes

Reduce Brightness: Yes

Hardware Configuration:

UPS Installed: No

AC Charger Information:

Connected: Yes

ID: 0x0100

Wattage (W): 60

Revision: 0x0000

Family: 0x00ba

Serial Number: 0x007d37e6

Charging: No