OK, if you have an an oscilloscope. Set it to the horizontal scan rate, and look at the signal going into the grid 1 of the 10BP4 , should be a green wire, the wave there should be 30-40 PtP. If it's not, you have a problem with the video getting TO the CRT, but if it IS correct, you have a very weak CRT.
http://suzaku.live-evil.org/CRT-input.jpg
this is from the RCA630TSService manual, rather close to your TV, also used a 10BP4.