Problem Solved......Using Marclll's advice I added debug print statements to Galileo's SD.cpp file (see path below) and determined that the SD_MOUNT_PATH (/media/mncblk0p1) was not being found in the "mtab" file.
Path to Galileo SD.Cpp File
C:\Intel_Galileo_Arduino_SW_1.5.3_on_Windows_v0.7.5\arduino-1.5.3\hardware\arduino\x86\libraries\SD.cpp
I then did a "fdisk -l" and got the following results which did not look right in that the SD card was showing that there was 4 partitions.
I then used the SD Card Association’s free formatting software tool (SD Formatter 4.0 for SD/SDHC/SDXC - SD Association) to reformat the card on the PC using "Format Type" set to "Full (OverWrite)" and "Format Size Adjustment" set to "On". After I did this I then inserted the SD card back into the Galileo and did another "fdisk -l" command. Results are shown below and show that the SD card now only has one partition.
After reformatting the card I then ran the sketch again and this time everything worked like it should!!!
Without the help I would not have been able to troubleshoot this....thanks!