Hi and welcome @memoryman.
Like Phil says, you'll need a limiting lamp.
Also, please find and post the circuit/schematic here (or link) so we are all talking about the same thing.
You don't say why you replaced the power transformer (or do you mean the output transformer, valves to speakers?).
A way to approach this is to disconnect the primary of the power transformer and see if you can apply power without problems.
Then reconnect power transformer primary while disconnecting the secondary (at least the high voltage winding) and see if that will power up okay.
You proceed progressively like this, bringing up a section at a time until the problem appears; the limiting lamp saving you from blowing lots of fuses.
Something to have an initial look at though is the main HT rectifier, which looks like that bunch of four diodes being cooked by that power resistor. You will need to lift one end of each for a certain test (and be sure the main HT line is fully discharged first, lest you "shake hands with beef" stored in the filter caps), and you will need to test all four.
It's fairly unusual for filter caps to lead to fuse blowing without first going through a long period of degeneration, increasing hum and so on, but a boofed rectifier will do it for sure.