I repair these every day, 03-04 have this problem of cold solder ( made in Mexico ), the cluster failing to fire up is usually the 3 24Ω resistors clustered together to the right of the right speedometer background bulb.
Do not use an iron hotter than 750°F or you'll pull the copper foil off the board. Sometimes with the 03 the 2 bigger glass diodes above the speedometer motor will also get a cold solder.
If the PRND321 display is on but not the odometer then it's the lone resistor 1200Ω to the left of the voltage multiplier coil at the left of the tach motor
As far as your other problem, your cluster is suppose to shut down after 20 seconds, there's an electronic timer between the speedo motor and the 4 gauges to the right. This one is a bit more complicated to repair and will often necessitate the cluster board to overnight in the freezer to pin point. Did 2 yesterday that wouldn't fire up, they haven't called back to complain. Do not attempt any of these repairs if you are not familiar with a fine point low temperature soldering.