Here are a few comments and suggestions.
Normally, the Clip Sport can be turned On (or Off) by holding down on the Power/Select button for 3 sec (and then let go).
(Make sure your device has at least 10-20% charge. Try connecting to an A/C charger via USB.)
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Maybe eject your micro SD card and then see if your Clip Sport starts normally.
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Maybe try connecting your Clip Sport to your PC,
If your device connects normally, try reapplying the Firmware file (should be named upgrade.hex)
- Maybe try applying the previous working version of the Clip Sport Firmware (1.36).
I think the previous version (1.36) is still available at this link
http://downloads.sandisk.com/firmware/clipsport/136/upgrade.hex
Please write back and let us know your progress.