My camera just flickers for one second, then nothing else happens. No display or anything. battery is charged.

Nothing wrong with the camera I guess. One ore more batteries in your camera are empty, and possibly they can't be charged (enough).
When you have rechargeable batteries for your camera, try charging the batteries again, but if the error returns, just buy a set of new AA rechargeable batteries. That should solve the problem.

This only happens when the camera has a serious problem. Next to turning off the camera, you also could remove the battery and charge it, before placing it back. Also check all contacts of the battery and memory card. Don't forget to close the battery door correct, after you charged an replaced the battery.
Make sure, nothing can obstruct the movement of the lens when the camera is switched on.

The internal battery, which is kept charged by the removable battery, has probably run down. Take it to a repair facility.

The internal battery charger may have failed and is not charging your battery. External chargers are inexpensive. Buy one and charge you battery on that and see what happens. If the camera works with the externally charged battery, I would do nothing further. Why pay for a repair that you can live without? If that does not solve your problem, the camera may need to go in for repair.

Before doing anything else be sure the battery is actually capable of holding a charge. Worn out batteries charge very quickly in the charger. A healthy battery will take several hours to charge.

When a "charged" worn out battery is put into the camera battery voltage drops instantly when the camera tries to start from it - nothing happens in this case.

Maybe you drop your battery and they have electronic components inside that could be spoiled, if is that the case, try to change the battery, it appeares to me that the ammount of current the battery is sending to the component is very low even thoe it seems to be fully charged that's why the camera is unable to display anything and the "busy" warning is blinking all the time, I hope you find this usefull.

maybe its a dead battery or scratch the oins of battery and cam

contact NIKON BAD CCD PROBLEM !

Get ir repaired free of charge just call them thousands face the same problem and all brands are repairing it free go call them

see the link for widespread Bad CCD problem dont worry if u are not on list but u have the same problem call them PLS RATE ME FIXYA for help !!

http://www.imaging-resource.com/badccds.html

Have you contacted Sony ? Mind you, they're only £30 on Ebay
https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwiaqJSyvufSAhXBwBQKHd_5A88QFggoMAI&url=https%3A%2F%2Fwww.sony.co.uk%2Fsupport%2Fen%2Fproduct%2FDSC-S75&usg=AFQjCNGtDo46s1BirFFcHHl2gDk_CjimYw&sig2=gP0XAe9rcDk9JdLADkI6ig

sounds like your ac plug to the laptop might be loose you can try ans see if you can resolder it back. the other problem is your ac cord might be broken wiggle it around see if the light flickers.