Hi Larry -
Your Nuvi 765T should light up when you connect it to your computer's USB port. If it doesn't, there may be a problem with the USB port. Try connecting to the other USB ports on the computer (or a different computer - such as one at work, etc.) if needed. This will help rule out a defective USB port on the computer. You can also connect to a USB charger for another device that you may have instead. It may not charge with another product's USB charger if it provides a very low power output though. The auto plug will not charge the Nuvi when it gets into this condition. Even if it does not light up, leave it plugged into the USB charger / or port over night.
Check the GTM20 traffic receiver plug. It has two LEDs on the body. The one closest to the power cord end is the Traffic Reception Status light and the the one closest to the plug end is the Power light. If either of these lights is on when connected to the Nuvi, the fuse is good. If not not, you may need to change out the fuse in the FM traffic receiver plug. The plug powers both the traffic reciever and Nuvi. Carefully spin off the bright metal ring to disassemble the end to access the fuse. Replace if it is open / blown. If you need replacement parts, they can be purchased from Amazon
for about $6.
After charging over night via charger or USB port, disconnect the nuvi from the power / USB cord and turn on by sliding AND holding the power switch in place to turn it on. Keep it held in position for 10 - 15 seconds before letting it slide back. During this time, the Nuvi should start up.
If it will not power up, the battery may be unable to accept a charge. You can replace the battery yourself, but it requires a steady hand, jewelers tools, good eye sight and patience from people selling parts to do this on eBay for as little as $6. Here's a link
to those auctions.
If you'd prefer not to do the work yourself, a second option would be to let Garmin handle the "repair". Your 765T is likely out of warranty, and garmin offers a "flat rate repair" fee of $99. If you opt to do this, you will send your 765T to garmin and they will send you a different 765T that has been factory refurbished; complete with the most recent maps available already installed and a gaurantee good for 90 days. Not a bad deal when you consider the cost of upgrading just the maps one time on the 765T. You can start the process on garmin's site, linked here
. I have used this service myself and was quite happy with it.
I hope this helps & good luck!