What does your TV instruction manual say about mains operating voltage range ? If you've only got 290VDC across your bulk mains smoothing cap and then that is eqivalent to 200VAC from a sinewave source. If your TV is specified to work from lets say 210VAC to 250VAC for example the the under volts lock out on the primary side switcher will say no go at 200VAC. For 230VAC mains you should expect something like 340VDC across your primary side bulk smoothing cap.
From the scope measurements it looks like your quasi sine inverter isn't really up to the job, the peak voltage isn't high enough it should be 340VDC not 290VDC. If there is a volts adjust pot in the inverter try tweaking it up a little bit but do it on an incandescent bulb load first.
As regards the TV psu, the primary circuit is very simple to trace out, it's marked out on to the top side silk screen, fuse, X cap, 2 Y caps, common mode choke, 2 Y caps, X cap, common mode choke, bridge rectifier and bulk smoothing cap with a few series ferrite beads added in for good measure.