Heat Pump doesn't work in AC mode, but heat mode is fine
Your blower motor's HIGH speed died

Most furnaces and split-system air handlers run their blower at a high speed in FAN and COOL, and at a lower speed in HEAT. As a result, it's possible for the blower to work when the system is set for one mode, but not the other.  I would consult the manual for your existing air handler/furnace for instructions on changing the blower speed used during cooling and fan-only operation.  This will change the latent/sensible balance during cooling, but will at least keep you running until you can get the blower, or the whole system, replaced.