Can I charge a Casio Exilim battery throug USB to my PC

The EX-Z77 is not a battery charger. It does not charge via the USB port. You need to remove the battery from the camera and put it into the supplied battery charger.

If you need a manual, you can download one at
http://support.casio.com/pdf/001/EXZ77_e.pdf
The battery charging instructions begin on page 36.

If the usb light functions, the problem is with the camera. Because it accept the charge but cannot deliver it to the battery. I think the problem is with the charging circuit, because it is in the camera, not the charger.

http://support.casio.com/download.php?rgn=1&cid=001&pid=167

http://support.casio.com/download.php?cid=001&pid=145&rgn=1

The above links have firmware updates, as well as, the general viewing and processing software of your camera.

You cannot charge your battery using a USB port. You must use the Battery Charger (BC-11L) that came with your Casio Camera.

I called casio and they told me that when you have a red flashing light on the charger it means the lithium battery is no longer any good. They offered to send me one free of charge. It's been several weeks and I have yet to receive it.

Tear off two small pieces of aluminum foil, each one no larger than a fingernail. Fold each one into the same size as the contact points on the Casio Exilim battery you want to jumpstart. Place them on that battery and press them onto the battery contact points. The aluminum foil pieces should protrude enough from the Exilim battery to touch the jumping battery. Then take a 9-volt battery, match the positive and negative terminals to the Exilim battery, and press the 9-volt onto the pieces of foil that protrude from the Exilim battery. Keep the batteries together for about 30 seconds; you may feel the Exilim battery become slightly warmer. Then put the Exilim battery into the charger; you should now see a steady red light with no blinking. This method worked for me.

buy a new battery (DUH)

I gave my wife also one of the Casio Exilim cameras. She doesn't take a lot of pictures. But so far the battery has not failed us. There might be a chance that your battery has died on you. I suggest you go to Casio and ask them to test the battery. I'm guessing it is the battery that has conked out. If it isn't then you need to have Casio check on your camera.

possibly with the usb cable but most likely you have to get the charger. http://www.amazon.com/Casio-Exilim-EX-Z75-Replacement-Battery/dp/B00125VCF4

Blinking light means charging error. Call tech support and they will replace battery for you for free.