From the description you given, there are two separate issues with this camera.
First, the Cyber-shot camera that you must have purchased around 2006 was actually made in 2005. You are limited to 1gb cards for the best operation. 2gb cards will work but have a tendency to corrupt easily in units this old. It is not designed to read SDHC cards. That is why it hangs up on the Sony Screen when the larger card is inserted. It is much safer to stay with memory cards that are 1gb or less.
One of the best places to purchase the smaller 1 & 2gb SD cards is on Amazon.com.
The second error appears to be a "lens error".
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 life of the camera (more than 3-5 years, yours is 8 or 9) then the power capacity of the battery may not be high enough anymore to handle the increased load or the battery does not really charge deeply anymore, meaning the power dips immediately under load. Because age is the big factor in battery health, even if the two were equally alternated in use, a new battery may be the answer. Batteries for your model are also available on Amazon.
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.
Lens errors are a common problem. Dirt can get into the gears or the lens can become misaligned from being carried in pockets, purses or at the beach. 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. The two links below give step by step DIY instructions on troubleshooting and attempting to fix this problem. A 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. Copy and paste the links into your browser.
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 the "do it yourself" approach doesn't work out for you and you need conventional repair, please let me know.
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