Hiss and Hum

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Computers and phones put out a lot of electrical noise.

Check all the shielding in the guitar.

Start with shielded cable from the volume pot to the jack. Twisting the wires does nothing or we'd all use a twisted pair from the guitar to the amp.

I have two identical LP HH guitars, both fully cavity shielded and jack wires are shielded cable, but the one without covers has a lot more noise than the one with covers while trying to record next to the computer. You can test if this is the problem by making a 'tinfoil hat' for your pickup(s) and running a ground wire from them to the jack ground or guitar cable outer grounded case at the jack. Lift and replace the ground connection and you'll know if that is the issue. Be careful not to damage any pickup winding wires or short out the pickup connections or it will be really too quiet...

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When you touch the tip of the guitar cord while plugged into the amp it should make a noise because you are grounding the hot wire (tip) that's normal. Did you try a different guitar cord? It never hurts to try a different tube but I think it's something else. I know you said that you tried the amp in another room. Was the room right next to the original room? If so it could be on the same circuit. Try taking the amp to a room far away from the original one. Maybe the kitchen or something.
Does the amp make the same noise without anything plugged into it? The other option would be to take the amp to a friend's house and see if it makes the same noise there.
Just trying the process of elimination. The only real way to track down the problem would be to put it up on the bench and test it out. That way you would know for sure if the amp was the problem.

 

Did you try powering your pedals off of batteries?
If it's fine when you play with just the guitar into the amp then the amp isn't the problem. Try plugging in one pedal at a time and use batteries to power the pedals. If it's quiet try the power supply - if it's still quiet move on to the next pedal.
Can you tell us what pedals and patch chords you are using? Some are noisier than others.

 

Sounds like you have a real problem with your AC service. Dirty power IS a thing.

 

I don't know if a power conditioner would help or not.

 

Your standard everyday one's won't. There are a few out there that use transformers that can isolate and clean the power but they are very expensive.
Not practical in this situation.

 

I figured that as well. A home based unit won't be cheap, and may not do the job needed. We had all of our theaters' power run thru isolation transformers. Pricey, indeed, but at least, they worked. Part of the issue was half of our juice came from the campus' generating plant, and the other half from the grid. With all of the offices and other facilities in our buildings, elec. noise was a serious issue. When we had to work with power from mobile generators, the noise was even worse. The new generators weren't bad, but the WWII military surplus units were horrid.