I couldn't get the schematic zoomed in enough to cite part nos, but the problem is almost certainly in the phase-shift oscillator triode which is in the lower left. Note the three caps in series, from the plate to the grid of that tube. That's the tell. Phase shift oscillators are not reliable starters, usually they have to build up a tad to get going. The flipside is, if any of the 3 series-caps are leaky, you can have trouble.
First, see if you get a small, 1/2 - 2 volt reading on the cathode. That shows the tube is conducting. If it is, the usual culprits are those series caps. You say the e-caps were replaced, but probably the various .01's and .02's scattered about the amp may not have been. If those caps are the originals, they could be leaky and that WILL cause stating problems. Still, before you change them out, if the shared 12AX7 triode is weak, that could also be another cause. If you have a known really fresh new one, swap that one in. Of course.....it could be BOTH the tube and the caps. Obviously you want to try the easy stuff first.
Phase shift oscillators are weak starters and weak caps or weak tubes can prevent the thing from starting up. Just for fun, I have built PS oscs on breadboards and changing the 12AX7 (highest gain in the series) to a 12AT7 (less gain) and it won't start or it might take 5 seconds to start. A 12AU7 (lowest gain) and it will not oscillate at all. They need to have everything going for them.
You are actually lucky if this is your problem because it is a pretty easy thing to isolate and troubleshoot.