I find that it helps to go through the basics with a new amp, checking all the little things to ensure that everything is in order. Make sure that you have a good set of matched power tubes. It helps to break down big sections into subsections that can be examined one by one. Don't take shortcuts. Sweat the small things first.
Make sure that the amp is unplugged and the caps are discharged and the amp is safe to work on. Search for "discharge sticks" or "discharging an amp". When the voltage of each power supply electrolytic cap reads zero volts to the chassis, the amp is safe to work on.
Clean the amp, apply deoxit to the tube sockets, tube pins, jacks, and pots. Make sure that the tube sockets are clean, sometimes it takes more than one application and some scrubbing. I use interdental brushes that you can get at a drug store. Pipe cleaners also do a good job but the brushes are best.
Remove all the tubes. Check out the hum pot with an ohm meter. Read between the center terminal and each side terminal. Move the pot and see if the resistance changes. The resistance across the outer two terminals should be around 100 ohms. Set it in the center with center to each outer balanced, around 50 ohms. A bad hum pot can cause all sorts of problems.
Power up the amp, turn off the standby (playing mode). Using a voltmeter, measure and record the AC wall voltage. Then read the 6.3VAC heater circuit, the 5VAC tube rectifier voltage, then each leg of the high voltage secondary to the center tap. The heater circuits should read 6.3VAC and 5VAC, the high voltage will vary. Some schematic have what the voltages should be. The earlier models were 375-0-375. These voltages will be higher if your wall voltage is above 117VAC. Taking these reading will tell you if your transformer is blown.
You can take resistance readings on the power transformer. The AC primary side should read about 2.5 ohms. The HV secondary should read around 55 ohms from the center tap to each of the two legs.
Let's assume that your transformers are working properly and your power supply caps are good.
When the amp is first turned on and the capacitors are not charged, there is big surge of current until the caps are charged. If the surge is too high, it is going to blow the fuse. Resistors can be used to limit the inrush. There are also devices called inrush current limiters that can be installed. This would help with the diode rectifier blowing the fuse. Some rectifier tubes, like the 5AR4, also limit the current inrush. I suspect that if you installed a 5AR4, the fuse will not blow.
The first 30uF cap that you mentioned might be bad (shorted) or the value might be too high. 40uF shouldn't cause a problem. If it is much larger, your initial inrush current might be too high for the fuse. A large capacitor can also cause what is called flashover in the tube. If you turn on the amp and see a flash i the rectifier tube you have a problem. It can cause the tube to blow. It can be fixed by adding a couple of diodes. I add them on my amps and they do a good job
The charing on the solid state module might be a sign of a problem. You can find a schematic for one here
on Weber's site. Diodes conduct in only one direction. Connect an ohm meter common (black wire) to pin-8. Connect the red wire on the meter to pin-6, and then pin-4. They should read almost zero. Reverse the leads and they should read infinity. Some diode rectifiers are more sophisticated. They have resistors and current limiter built into them. This type produces slightly different results when you test them. They can be found on the Weber site. They are called Copper Cap Rectifiers
You can also plug the solid state rectifier in and read pin-8 to ground (the chassis). You should see something like 470VDC. Again this will vary depending on your wall voltage.