Is it set to Fullscreen (Open Chrome and Press.. F11)
If not, See -> http://www.google.com/support/forum/p/Chrome/thread?tid=652fce5918e2ba13&hl=en
To Enable Password when returning from Sleep see below:
OP1: http://johnsonyip.com/wordpress/2009/11/21/how-to-password-protect-wake-up-from-sleep-mode-in-windows-vista-to-enhance-your-pc-security/
OP2: http://www.vistax64.com/tutorials/63567-power-options-sleep-mode-problems.html
The Turning off Thing sounds Like Running Processes..
I'd Run some Scans on it to make sure it's not Infected.
► Virus/Malware Removal ◄
Plug a Ethernet lead from your Router/Modem to the Computer..
Pic -> http://www.google.co.uk/search?hl=en&client=firefox-a&hs=Ki2&rls=org.mozilla%3Aen-GB%3Aofficial&biw=1280&bih=790&site=search&tbm=isch&sa=1&q=ethernet+leads&aq=f&aqi=&aql=&oq=
Restart and keep pressing F8 Or F5.. Select Safe mode with networking..
When it loads Download & Run These: (Direct Link's -No Hassle-)
RKill -> http://download.bleepingcomputer.com/grinler/rkill.exe
And TDSSKiller -> http://support.kaspersky.com/downloads/utils/tdsskiller.exe
That will Automatically Remove Known Malware Blocking Your Security.
Then Download & Install Both Of These (IMPORTANT - Update Both)
http://download.cnet.com/Malwarebytes-Anti-Malware/3000-8022_4-10804572.html
http://download.cnet.com/SuperAntiSpyware-Free-Edition/3000-8022_4-10523889.html
Then Run Them both, And scan the Entire Computer.. Remove any Findings.
You Can Also Download & Run CCleaner -> http://download.cnet.com/ccleaner/
Run it and do 2 scans in sections.. Cleaner & Registry.. Remove any Findings.
Fix Windows File Associations -> http://www.addictivetips.com/windows-tips/fix-windows-7-file-association/
Hope it helps :)