Hard to tell if your pins are ok from the image. The only real way to tell for sure is to check with a multimeter. Do you have a way to check electric continuity?
Another possibility is that your cable broke. Do you have another cable that you can test with your vita? Or a friend that has one maybe?
Could be your power brick. Try your cable with any power adapter that has 5V on it that also has 1.5A or higher (2A is fine 3A is fine, 1A is not enough to charge the vita).
I would highly suggest finding another cable and brick to try to make sure it's not those.
To be sure it's your pins, you will need a working vita cable and the multimeter. You will also need to take the motherboard all the way out... which means a full vita dissasembly. Then you connect the motherboard to the cable and check continuity between a few spots on the board and the usb end of the working cable.
Red is vcc 5v
Black is gnd
Green is D+
White is D-
Vita 1000 board at the port area.
USB color pinout
When the cable is connected, the none of the colors should share continuity. Red should only be connected to red. Black should only be connected to black. Same with Green and White, no connection to other colors (with the cable already plugged in ).
Then also make sure the Red on the board is connected to the red on the end of the USB cable. Be sure with all colors, the White on the board is connected to the white at the end of the cable, the Green on the board is connected to the green on the cable.
If any of the different colors are connected, or if the cable end colors aren't connected to the colors on the board. AND you are sure you have a good cable... Then your port is screwed up.
If your port is screwed up you have a few options.
1. Get it fixed.
2. Buy a replacement mother board from Ali-Express.
3. Mod a different port to the vita. (micro usb or usb-c recommended).
If you decide to mod a different port, I don't suggest adding the green and white data lines unless you have a microscope. Just the red and black pads for power and thus charging. You would be limited to FTP for data transfer or removing the sd card if you use an adapter with a computer.