My first inclination is to assume that a lens error is the problem itself, but first, there is one more likely possibility, lack of sufficient power. Remove the battery, check the pins or connectors in the battery compartment, and make sure that they are positioned correctly to contact the battery. Then use a q-tip with alcohol to clean and dry them. It is also a known issue that digital cameras circuitry can also become much more sensitive to the lower power level produced, so if you have been using the same rechargeable battery for the life of the camera (more than 3-4 years), yours is around 10, then the power capacity of the battery may not be high enough anymore to handle the increased load. A new battery may be the answer.If the above does not solve the issue please continue as it is very likely that the problem is a lens error.
Even if the lens extends, it is quite possible that it does not make it to the correct sensor point due to an obstruction like a grain of sand or residue build up. A lens position error will halt the camera start up process.
The lens error indicates that the movement is inhibited possibly by sand or grit. It also may be misaligned or an internal component has failed. Here are a couple of links to some other things to try. With newer cameras I am usually hesitant to suggest these options since they include some more extreme procedures that may cause further damage if not done correctly, but since yours is probably no longer under warranty, they may save you an expensive repair bill. An older Canon camera is used to demonstrate these procedures but, the lens structure of these compact cameras is the same so the examples do apply to this unit. These procedures are effective about 60% of the time. Click on or copy and paste the links into your browser.http://www.e18error.com/repair.htmlcamerarepair.blogspot.com/2007/12/fixing-lens-error-on-digital-camera.htmlIf the "do it yourself" approach doesn't work out for you please see the note below.
Note: Considering the age and present value of this camera, paying the cost of having it repaired , approximately $75 - $90 (if the parts could be obtained) really is probably not very cost effective. The standard "rule of thumb" is if the repair cost is greater than 50% of the value of the camera, it is not worth it. A used or refurbished Powershot SD600 can be purchased online for about $15-$40
Please keep in mind that my diagnosis & solutions provided are directly dependent on the accuracy of your description of the problem. As with any "do it yourself" fixes, success is a "team effort", since I can't see or touch the camera, and relies on the customer's manual dexterity and ability to follow the instructions well.
If you require additional information, please use the Reply to Expert Tab to contact me. Click the ratings only after our exchange is complete and you are satisfied.
If you are satisfied that my answer is accurate or has provided a reasonable alternative, please do not forget to rate my answer OK, Good or Excellent.