I love the SG guitar and have three SG types: two Epiphone SG's and an amazingly great sounding inexpensive LTD Viper 50 SG copy.
Sounds like yours is silent.
Sounds like the amp has a grounding problem with the power supply or something. Is this a Vox DA5, great little amp?
Yes it's the Vox DA5, I usually stay with reverb and clean 1 pos, even on 1/2 watt you could damage your hearing over time. I have just tried different wall sockets, no improvement, changed cables I have 3 of, the better quality heavier cable did make a bit of improvement but not acceptable, no change with the other shorter cables, still very noisy, changed the PSU AC, I had a spare, no improvement, but for some reason I played around with the Vox controls and found by turning my Vox tone control down about half way no noise, but any where between half and full treble it's very noisy, ( Static and hum ). Static is not there as long as you play or simply make contact with any metal part on the guitar, although there are a lot of confusing issues I'm convinced it is the Vox. BTW I nearly bought a Viper SG but the idea of building a kit appealed, then this kit came up on Ebay, and you know the rest, the main part that worried me a bit was gluing the neck, but all went well using the proper glue, changed the strings to D' Addario's. Just in case I'm going crazy I tried the SG on the Tube amp again and no problem all quiet, then Strat on the Vox same problem static, I'm sure the Jury can only come to one conclusion, the Vox is guilty.
Anyhow thanks very much again Duffy for your input and time spent here.