Some tellies can be pretty difficult to see with the torch trick the angle can be critical too.
If it was me I'd be concerned about getting the backlights working first, a no picture can be pretty much anything.
Seeing you have swapped the inverter the only thing then is to ask is the inverter being told to switch ON, there is usually a pin marked 'Bon' (backlight ON), I usually use a clapped out battery from a battery pack, about three volts is ample, providing the main voltage is up around 24V, the inverter should fire up with about +3V on the BLon pin and the negative lead on the metal work, that is how I test them sometimes, if you got doubts you can add a diode in series as a 'DC blocker'.
One thing you don't want overlook is sometimes the tubes are clipped in, I've seen them burn occasionally.... sometimes the tubes crack on the end, had one or two like that, I recently repaired a 23" Tesco Wonder Telly with cracked tubes... so I fitted a LED converter kit I got from Ebay far, far cheaper and reckon the picture is much more crisper.
Tesco Wonder Telly's are great...... nick the inverter and use it as a tube tester it'll fire up as soon as you apply 12V DC - Just an idea to throw some light.
I'd be tempted to try them tubes
Dave