Assuming you have already verified the game files in Steam, how about starting it, then walking away for a while.
Given that it's your first run since downloading, it may take a long time to install and get going. How about starting up the game, then leaving it to do its thing for 20 minutes and see if that makes any difference? If not, check Task Manager and see if the exe file is still running.
Also, this may be an exceptionally stupid question, but do you have a DX10 capable graphics card?
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Ok, so you've definitely tried the "Verify game" option.
Reboot your PC, and run Hitman: Absolution again. Leave the PC alone for a good amount of time (20-30 mins) and see if anything has happened.
If not, check Task Manager, to see if the exe file is still running.
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Well, apparently it supports DX11, so that shouldn't be an issue.
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Did you try my suggestion of rebooting the PC, starting Hitman and waiting 20-30 minutes?
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Have you tried asking this question in the official Steam game forums?
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hitman Absolution Failed to start (game app already running) plz HELP ME
System Information
Time of this report: 3/30/2013, 20:00:44
Machine name: Y470-PC
Operating System: Windows 7 Ultimate Edition 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_gdr.130104-1431)
Language: Chinese (Simplified) (Regional Setting: Chinese (Simplified))
System Manufacturer: LENOVO
System Model: 20090
BIOS: InsydeH2O Version 03.60.4147CN31WW(V2.09)
Processor: Intel® Core™ i5-2450M CPU @ 2.50GHz (4 CPUs), ~2.5GHz
Memory: 8192MB RAM
Available OS Memory: 8136MB RAM
Page File: 3587MB used, 12682MB available
Windows Dir: C:\windows
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: Using System DPI
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.01.7601.17514 64bit Unicode
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