Try "About This Mac" under the Apple menu, select System Report, and look for the info about Card Reader. Do you see something like what is shown below?
In all likelihood, if it won't read any cards at all, it is damaged or broken. However some things to check first (after each one, re-check to see if you can access the SD Card:
Shut down your Mac, then restart it. You have probably already done that.
Go to Finder > Preferences > General, make sure the "External disks" option is ticked. This will make the SD card show up on the Desktop. See if it appears. Also, select Sidebar tab on the top, make sure the "External disks" option under Locations is also ticked.
Reset NVRAM: shut down your Mac, then turn it on and immediately press and hold Option + Command + P + R. Keep holding down those keys for about 20 seconds. Then release the keys and allow your Mac to boot up.
Open Disk Utility. See if the SD Card shows up on the left side. If it does, Mount it through Disk Utility.
Some Apple Authorized repair centers (not Apple Store) will endeavor to repair or replace even older units and devices.
Last resort if the built in SD Card Reader is still inoperative: purchase an inexpensive external SD Card reader and use it in one of your USB ports.