Try starting up the phone in "Safe Mode" and see if you can access the SD card while in there. NOTE: Not all apps will work in "Safe Mode", so if it is a particular app that is having problems accessing the card, then you will need to try accessing it with an app that will work in this mode. Also, if it is just a singular app that can't access the card, then it may well not be the card that is the problem, but the app.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.