I am using Samsung Galaxy Nexus on Verizon mobile with Android version 4.2.2. I tried to connect my device to a PC via USB cable and through the cable the charging process is on but it doesn't show the notification and it is not working with media transfer. I installed all the drivers like Samsung Kies, adb driver, usb driver, but still I can't connect. I tried the process with developer options too, and nothing happened. Please help me. Do I need to download any APK files for the device?
If you don't get a notification on the phone, it means there's no USB connection. The most likely cause for this is that the cable you're using is not a real USB cable, but only has the power wire inside the cable, with the data pins not connected to anything. Devices that use USB to charge sometimes come with such cables instead of real USB cables because they're cheaper to make. Physical damage to a normal USB cable (e.g. by shutting it in a door or under heavy furniture) can break the data connection but still leave it able to supply power.
Try using another USB cable and see if the notification appears. If that doesn't work, then probably the problem is caused by a damaged USB port, either on your phone or on your PC. Try a different port on your PC. If the port on your phone is physically damaged, all you can do is take it to someone who can repair it.
Alternatively, you might not need to use USB at all. There are many apps that can transfer photos, contacts, or other data between your phone and PC over Wi-Fi, without needing a USB connection.