iMac 27'' mid-2011 stuck on startup (grey screen)
You probably need your video card replaced. See this Apple article regarding a known video card issue:

https://web.archive.org/web/20130820015305/http://support.apple.com/kb/TS5167

From the article:


  Apple has determined that some AMD Radeon HD 6970M video cards used in 27-inch iMac computers with 3.1GHz quad-core Intel Core i5 or 3.4GHz quad-core Intel Core i7 processors may fail, causing the computer’s display to appear distorted, white or blue with vertical lines, or to turn black. iMac computers with affected video cards were sold between May 2011 and October 2012.