Hi Shane and welcome to the forum.
You have one of the early valvestates there and these were notorious for poor soldering.
One of the major areas is the power supply where there are two 15 v zeners (ZD1 & ZD2) and associated
5 watt wire wound ceramic resistors (R101 & R102) which look like small oblong blocks of cement !
They are near the power switch.
Depending on the heat damage Its usually necessary to have some decent tools soldering iron etc
to be able to do a neat reliable job if this area needs repairing.
The zeners provide plus and minus 15 volts for the IC's to operate and sounds like to me with no line out
that the pre amp is not working .
If it has no power there this would explain it.
The tube only works on the second channel and it's heater or filament will light up as it gets its power
before the zeners and resistors.
I would have thought the power amp would hum slightly into the speaker without the pre-amp section.
If there is a lot of track damage it may be eaisest to buy 2 more zeners and 2 more resistors and take advantage of
the length of the connection wires to bridge broken tracks underneath.
You should be able to measure the two 15volt supplies between ground and one side of the resistors.
On one end there will be 20 something volts and 15 on the other.