Congrats on your new purchase.
You didn't state which Model S. Perhaps a 75 or 75D? Assuming an S75, which originally had 249 miles of range, 170 seems quite low (68%). Did you charge to 100%? Are there any error messages?
When using the Mobile charger, what color is the ring on the charge port? Do you get any error messages in the car? Depending on the charger (likely Gen1) the charger box on the plug side has LEDs. Do these light up and are they green or red or flashing red? For flashing red, count the number of flashes between pauses. The manual has more details on what the different indicators/flashes mean. If no LEDs light up, are you sure the plug you are using has power?