Is that the voltage under load, or disconnected? I just built the Millet amp and it works wonderfully. My wal-wart puts out around 32V if it is not connected to the amp, but when it is powering the amp it is down around 26V. That is the nature of an unregulated wal-wart. To be absolutely safe you could buy the popular regulated Elpac 24V adapter for about $30. I use it for my Meta42 and have also tried it with the Pete Millet amp and it stays at 24V whether connected or not and seems to work just fine with the Millet amp.
If it is 34V when connected, that could damage the tubes. The heaters are spec'd to take 16V as a maximum, and each heater will take half of the voltage since they are wired in series. However I really doubt your wal-wart would put out 34V when connected to the amp since the heaters draw 150mA which is a decent load. And in any case Pete has put in protection in the form of the PTC fuse and transient suppressor which should work together to cut off the PS if it exceeds 30V.
Reading your other thread leads me to believe something very wrong happened. If the LED is not coming on, either it got fried or there is a short from V+ to V- somewhere in the circuit, or the V+ and V- somehow got reversed. The things to check:
1. Make sure that V+ is not connected to V-. I would measure from the V+ Leg of the DC jack (the one that is at the back of the jack) to the hole that is right beneath TP2. Either measure the resistance (which should be infinite) or use the beep function and make sure it doesn't beep.
If this is the problem, that V+ and V- are connected, the components I would desolder and resolder first are the Buffers, the DC jack, and perhaps the LED, since it is at these locations that the V+ and V- are right next to each other and there could easily be a solder bridge.
2. The value of the resistor that is next to the LED. Should be somewhere between 1.5k to 5k. I use 2k.
Once both of these check out, then plug in the wal-wart, throw the switch, and see if the LED lights up. Since the LED could have died, also check the Voltage from the back of the DC jack to TP2, it should be between 24V-30V. If that checks out you may need a new LED. I would try to get to this point before you do anything else, because without the PS working nothing else will, and the LED is a good indicator of a working PS.
Also I am willing to personally take a look at your board if you get to the point of giving up on it.