Replacing Non-Working Single-Pole Dimmer Switch
I'd be surprised if the wires coming in from the bottom of the box (the 14/2 NM) weren't the supply (hot).  It's fairly common to use a 14/3 for the run between the switches and the light\fan. In that you only have 2 cables coming into the box and you're working with single-pole switches, the easiest way to verify is to use the regular switch to test for the hot.  

I'd connect one of the non-green terminals to the red wire coming in from the top and one of the non-green terminals to the black wire coming in from the bottom. Switch it on, and turn the breaker back on. My guess is that either the fan (most likely) or light will come on. 

You can then confirm this by turning the breaker back off, removing the red wire from the switch, and replace it with the black wire coming in from the top of the box. Turn everything back on, and the other device should be on now.

After you've confirmed that the bottom black wire is the hot, follow the installation instructions on the new switch and dimmer. You'll need to connect both of line terminals on the switches to the hot. You can either jumper them (tacky) or wire-nut two pigtails onto the hot and connect one to each switch.