Can drain voltage/current affect gate voltage of MOSFET?
Your equation Vds = Vg - Vt is not correct. The relationship between Vds and Vg will actually determine which region the transistor is operating in, if Vg is greater than Vt:


Vds &lt; Vg − Vt    =>The linear region, where it acts like there's a resistor between the drain and the source (as Vds increases, Ids increases linearly).
Vds ≥ (Vg – Vt)   =>The saturation region, where an increase in Vds only results in a small increase in Ids.


In your case, Vg is unexpectedly at the same high voltage as Vds. If Vds is dragging Vg up, it's because there's been permanent damage to the transistor. This doesn't sound like the most likely cause of your problem, or at least the root cause. The board shouldn't have been designed to operate with Vds much greater than Vg, and it probably wasn't.