GE L-660 tubes don't work.

[HiFiCanada]

When I got the radio, I can easliy see that someone else has been working on it, but since that type of radio does not have a power transformer, I was not to worried about going ahead to recap.
I slowly powered it up on my variac, the dial light is on, but the tubes did not light up.
I checked all the tubes on my Heathkit TC-1 tube tester and they are all good, at least they all glow.
So my queston is that if all the tube glows on my tester, then if everything was OK in the radio, it should also light up.
I am a bit worried that a coil is open,the queston is that if a coil is open, should the tubes still light up?