In my Macbook Pro 15inch, late 2013, the SD card reader doesn't work after installing Yosemite 10.10.2. Doesn't load cards at all. Tried to blow out slot, fiddling with switches inside port, nothing.
How can I analyze and fix this issue
The first step is to open system information and see if anything shows for that device.
Next would be to install a clean OS on to a USB drive or back up and erase the Mac / reinstall the OS. You could try a safe boot, but I've not seen that make any difference for the SD card slot even though it could help if you had an oddball kernel extension conflict.
Also, be sure to test your SD cards on another computer or reader as it would be a shame to have that be the issue and have to restore a backup to find out that was the issue.