With the description of the problem that you have given, the only place to start is where you have already begun: Grabbing and pulling the lens. The available user DIY fixes, require some lens extension to be effective. Just to reassure you, I actually recently worked on the exact same problem with a Sony camera that took at least 4 hours over two days to get the lens to extend by catching it when it made the slight movement when turned on . It takes patience but is generally the only alternative since a conventional repair costs as much as a new camera. Once you get it even partially extended, you can use some of the procedures below to restore full operation.
If the lens does not make it to the correct sensor point due to it being forced in, as noted above, some physical manipulation is necessary. A lens position error will halt the camera start up process. Lens errors are a common problem. 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 they may save you an expensive repair bill or having to replace it. The links below give step by step DIY instructions on troubleshooting and attempting to fix this problem. 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 the link location and paste them into your browser.
If the "do it yourself" approach doesn't work out for you and you need conventional repair options and a value assessment, please let me know.
Note: Considering the age and present value of this camera, paying the cost of having it repaired , approximately $75 really depends on how attached to the camera you are. 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 A1300 can be purchased for about $35-$65 and a brand new one (with warranty) for as low as $76.
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, please do not forget to rate my answer OK, Good or Excellent.