Make sure that there's no password or security code set to the memory card. If you created a security code for the card while it's inserted to the phone, the card would never be detected by any computer or phone.
The question is, how do you connect the microSD card to the laptop? Do you have a built-in card reader on your laptop? Or are you using a USB card reader?
To isolate the problem, try using another card reader and connect it to the computer. Or, connect the memory card into another computer. This would help you to detect which is causing the problem
Answers & Comments
Make sure that there's no password or security code set to the memory card. If you created a security code for the card while it's inserted to the phone, the card would never be detected by any computer or phone.
The question is, how do you connect the microSD card to the laptop? Do you have a built-in card reader on your laptop? Or are you using a USB card reader?
To isolate the problem, try using another card reader and connect it to the computer. Or, connect the memory card into another computer. This would help you to detect which is causing the problem