MacBook Air (11-inch, Mid 2011) keeps shutting down immediately

My friend has a MacBook Air (11 inch, Mid-2011, OS X El-Capitan) that keeps shutting down immediately (in minutes). Tried resetting SMC. No luck. Tried Apple diagnostics (it shuts off during). Tried running Ubuntu via USB flash drive (it shuts off during). Any help will be appreciated. Following is the log.

Time stamp Domain Message Duration Delay
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UUID: (null) 2016-02-08 22:36:56 -0600 Start powerd process is started
2016-02-08 22:36:56 -0600 Summary- [System: No Assertions] Using Batt(Charge: 87)
2016-02-08 22:36:56 -0600 Assertions Kernel Idle sleep preventers: IODisplayWrangler
2016-02-08 22:37:51 -0600 Assertions PID 92(hidd) Created UserIsActive "com.apple.iohideventsystem.queue.tickle" 00:00:00 id:0x0x900000181 [System: DeclUser kDisp]
Sleep/Wakes since boot at 2016-02-08 22:36:56 -0600 Dark Wake Count in this sleep cycle:0

Time stamp Domain Message Duration Delay
========== ====== ======= ======== =====
UUID: (null) 2016-02-08 22:42:24 -0600 Start powerd process is started
2016-02-08 22:42:24 -0600 Summary- [System: No Assertions] Using Batt(Charge: 85)
2016-02-08 22:42:24 -0600 Assertions Kernel Idle sleep preventers: IODisplayWrangler
2016-02-08 22:43:00 -0600 Assertions PID 92(hidd) Created UserIsActive "com.apple.iohideventsystem.queue.tickle" 00:00:00 id:0x0x900000189 [System: DeclUser kDisp]
Sleep/Wakes since boot at 2016-02-08 22:42:24 -0600 Dark Wake Count in this sleep cycle:0

Time stamp Domain Message Duration Delay
========== ====== ======= ======== =====
UUID: (null) 2016-02-08 22:44:53 -0600 Start powerd process is started
2016-02-08 22:44:53 -0600 Summary- [System: No Assertions] Using Batt(Charge: 84)
2016-02-08 22:44:53 -0600 Assertions Kernel Idle sleep preventers: IODisplayWrangler
Sleep/Wakes since boot at 2016-02-08 22:44:53 -0600 Dark Wake Count in this sleep cycle:0

Time stamp Domain Message Duration Delay
========== ====== ======= ======== =====
UUID: (null) 2016-02-08 22:56:18 -0600 Start powerd process is started
2016-02-08 22:56:18 -0600 Summary- [System: No Assertions] Using Batt(Charge: 83)
2016-02-08 22:56:18 -0600 Assertions Kernel Idle sleep preventers: IODisplayWrangler
2016-02-08 22:57:10 -0600 Assertions PID 92(hidd) Created UserIsActive "com.apple.iohideventsystem.queue.tickle" 00:00:00 id:0x0x90000018e [System: PrevIdle DeclUser kDisp]
2016-02-08 22:58:07 -0600 Assertions PID 72(apsd) Released ApplePushServiceTask "com.apple.apsd-login" 00:01:32 id:0x0xb0000014b [System: DeclUser kDisp]

2016-02-08 23:03:51 -0600 :Showing all currently held IOKit power assertions Assertion status system-wide: BackgroundTask 0 ApplePushServiceTask 0 UserIsActive 1 PreventUserIdleDisplaySleep 0 PreventSystemSleep 0 ExternalMedia 0 PreventUserIdleSystemSleep 0 NetworkClientActive 0 Listed by owning process: pid 92(hidd): [0x000000340009018e] 00:06:40 UserIsActive named: "com.apple.iohideventsystem.queue.tickle" No kernel assertions. Idle sleep preventers: IODisplayWrangler