We were traveling with our garmin and the rental car was not charging the garmin as we thought it was. We think the battery might have run down. We have tried to charge it with our phone charger which has not worked and we also tried to charge it in our car but all it does is blink and go off. When we click it on it ony keeps blinking.

First, let me say that letting the battery run down completely does no harm in a rechargeable device. As a matter of fact, these types of batteries perform best in the long run if they are run fully down and charged fully up.
Try leaving the unit turned off and recharging for at least 1 hour, then power it up and see the result.
Gary

If what you say is right it would need at least 10 hours charge with at least 6 hours before you would even be able to see & do anything with it.

Charging with the phone charger will not really work, as the current supplied to a phone is way lower than a GPS. Even if it did charge it would take like 24 hours...

You will have to either get a wall charger or a car charger that you are sure is working and charging and leave the GPS on charge at least for overnite.. It should be Ok next day. If not, then you have a fault with the unit, for whatever reasons.