While we're not familiar with a Lenovo 9.25A power supply for a docking station (they're usually 6.75A/130W), the slim tip connection has a center "signal pin" that technically turns the PSU on so it can be used by the device (laptop, docking station, etc).

If this isn't working properly on your T440, or your T440 isn't recognizing the PSU, the PSU will not come on.

Depending on your region, these power supplies are fairly inexpensive these days

65W Laptop Charger for Lenovo Thinkpad T440 T440S T440P

MaxProAndU Team