Puede usar PowerShell para esto. 
Apagado
Get-WinEvent -LogName Microsoft-Windows-Diagnostics-Performance/Operational | Where { $_.Id -eq 200 }
Esto le dará una lista de los tiempos de apagado registrados. 
Comando alternativo, mejor optimizado para conexiones remotas: 
Get-WinEvent -FilterHashtable @{LogName = "Microsoft-Windows-Diagnostics-Performance/Operational"; Id = 200; }
Salida de ejemplo: 
TimeCreated Id LevelDisplayName Message
----------- -- ---------------- -------
2017-01-28 18:25:46 200 Critical Windows has shutdown
2016-11-01 19:55:21 200 Error Windows has shutdown
2016-10-29 00:18:38 200 Critical Windows has shutdown
2016-10-26 23:16:55 200 Warning Windows has shutdown
2016-10-26 15:37:40 200 Warning Windows has shutdown
2016-10-26 02:18:24 200 Warning Windows has shutdown
2016-10-26 02:10:34 200 Warning Windows has shutdown
2016-10-26 02:04:01 200 Warning Windows has shutdown
2016-10-25 14:23:11 200 Warning Windows has shutdown
2016-10-25 13:07:46 200 Error Windows has shutdown
2016-10-25 00:18:12 200 Error Windows has shutdown
2016-10-19 13:16:39 200 Critical Windows has shutdown
Arranque
El siguiente comando le dará una lista de los tiempos de arranque registrados. 
Get-WinEvent -LogName Microsoft-Windows-Diagnostics-Performance/Operational | Where { $_.Id -eq 100}
Comando alternativo, mejor optimizado para conexiones remotas: 
Get-WinEvent -FilterHashtable @{LogName = "Microsoft-Windows-Diagnostics-Performance/Operational"; Id = 100; }
Salida de ejemplo: 
TimeCreated Id LevelDisplayName Message
----------- -- ---------------- -------
2017-10-07 21:35:38 100 Critical Windows has started up
2017-01-28 18:25:48 100 Critical Windows has started up
2016-12-11 17:45:07 100 Critical Windows has started up
2016-11-16 13:26:52 100 Critical Windows has started up
2016-11-01 19:55:21 100 Critical Windows has started up
2016-10-29 00:18:39 100 Critical Windows has started up
2016-10-26 23:16:55 100 Error Windows has started up
2016-10-26 14:51:07 100 Error Windows has started up
2016-10-26 02:24:01 100 Error Windows has started up
2016-10-26 02:18:24 100 Critical Windows has started up
2016-10-26 02:10:34 100 Error Windows has started up
2016-10-26 02:04:01 100 Critical Windows has started up
2016-10-25 14:23:12 100 Error Windows has started up
2016-10-25 13:07:47 100 Error Windows has started up
2016-10-25 12:56:23 100 Error Windows has started up
2016-10-19 13:16:39 100 Critical Windows has started up
He probado esto en PowerShell 5.1 y en Windows 10.0.15063. Pero también debería funcionar en Windows 7, siempre y cuando tenga al menos PowerShell 3.0. Tenga en cuenta que debe ejecutarlo como admin. 
Encontrará la documentación completa del comando aquí  docs.microsoft.com