Making some progress with the 16K Microbee

[CheshireNoir]

From your text and photos, it appears that your 6545 CRTC is at least partially working.
When MWBASIC boots, it firstly initialises the Z80 PIO, then the CRTC registers, fills the screen RAM with spaces and loads the PCG with INVERSE characters.
So, if you're getting a stable picture of any kind then the 6545 CRTC is at least partially working. Seeing a flashing cursor is also a good sign; even better if it moves right and left with keystrokes..

If there's junk characters on your screen then there's and issue with char RAM access.

The boot beep come later immediately prior to the opening cold boot MWBASIC caption displayed.

Having an EPROM Emulator, a stack of EPROMs (or NVRAMS) with programmer is most practical way to fix bees as the enables one to write and use small diagnostic programs the simplest containing just one byte 0x76 - The HALT instruction.

Thank you someone,
That description of the bootup steps helps a lot. 
I've replaced all the sockets for ROMs and for the 6545, as well as the connectors between the base and the core board.
I'll try this 6545 in my other Microbee tonight, which should either confirm the 6545 is OK or give me something to work on. (I swapped the other way to no change but realised I didn't try this 6545 in a working 'bee. D'oh!)
Assuming the 6545 is good, I'll concentrate, initially, on seeing if I'm seeing "sane" logic out of the 74 series between the video out and the 6545. There's only two chips there and I should be able to probe them with the logic probe without having to bust out the oscilloscope. 
This has been a fun little project so far. So glad I have a spare Microbee to help me fix this one though.

Chesh