Hitachi 50ux58b

It's possible that the Convergence IC's are causing a shutdown of the power supply. Also on this model, there have been problems with:
C707 - 1000pf @ 2kv Cermaic Disc Cap (normally a small blue one) Hitachi Part # 0244211.
I901 - A STRM6811a Reg Ic and
E994 - 2.0 Amp Circuit Protector (Pico Fuse) having a high failure rate. If the 2 amp pico fuse was good, and the capacitor looked OK, then I would check the convergence circuit board. There are many other parts that can also cause shutdown problems, however.

If you have Hitachi model number 50UX58B, 60UX58B, 50UX58K, 60UX58K, 50SBX78B or 60SBX78B and you have the following symptoms you may want to grab a repair kit from www.TvRepairKits.com. They have put together a kit that includes the parts and instructions to fix these models. This is a fairly common problem with the above model numbers. It is typically caused by a blown capacitor and pico fuse. Again, you can get a kit from the above address. 
Here are the symptoms...

Primary Symptom: No Audio or Video. Power light will come on briefly then shut off.
Other Possible Symptoms : The green LEDs on the circuit board light up for a few seconds then turn off.

Hope this helps,