My advice? Hit the trails. There's nothing like a long, open track in front of a horses nose to inspire some forward.
My horse was like this when I bought him.
Basically you have to be really consistent with the ask/tell/make escalation of pressure. I would ask with a click of my tongue and a squeeze of my calf for for forward, no response. I then give a much stronger leg cue, strong seat cue, and another cluck, no response. My last step was over-undering with my reins (only thick cotton so it was more the noise and action). Once he was forward I made him stay forward, usingthe over-under if he tried to come back. I started out just doing this with a canter, as he could go as fast as he liked, but not slower than I wanted. Eventually they respond to the light cue.
What do you do on a hot horse who is touchy to the leg? Use more leg. So it makes sense that on a dull horse, you use less. When she is going forward, sit quietly. Only use leg when you want her to move off it, or move forward.