Just a bit of advice to the OP; it might be better for everyone if you organized all your questions into a unified thread describing what you have and what's wrong with it. This piecemeal approach you're taking to asking isolated questions about very specific technical details out of the blue makes it really difficult to follow what's going on here. (I mean, I assume you're asking here about the same machine in
these two other threads.)
There is a mod made for it to work with an old style e/i. Problem?
No. That's not likely to have anything to do with this behavior, especially if you're testing the machine without anything plugged into the expansion connector. (Although I guess if you want to talk about it, is this the only mod that's present, or does this computer also have a 5-pin DIN plug dangling out of the expansion slot hole that's connected via a few tack soldered connections to various places on the board? This would tell you if your keyboard had actually at some point in its life been paired with an expansion interface that required a specific set of hacks to work reliably.) What that mod does is convert a pin (39) that in the original Level I configuration provided a *very* current limited +5v output into a ground; Radio Shack did this mod by default on any machine they upgraded to Level II BASIC and it's expected to be there for any type of expansion interface. The only potential for problems is if you connected your keyboard to an expansion interface
that needs the buffered cable with a
plain cable. That would short the power that's fed to the buffered cable *from the expansion interface* to ground on the TRS-80. (The buffered cable isolates them.)
Anyway, regarding the photos of the screen you're showing, is that photo of the power-on state accurate, IE, does it really have those black drop-outs instead of complete characters? That would be very strange behavior because the TRS-80 screen hardware shouldn't need any software initialization to just spit out whatever random junk is in video memory when you turn it on. Are there flickering black streaks moving through the frame or other "dynamic" activity before you hit reset?
The second photo shows the display to be in 32 character mode vs 64 characters.
This would mean the bit on port FF that controls whether video is in 64 or 32 bit isn't being forced to zero... which would certainly imply that the machine isn't executing the BASIC ROM, since outputting a zero on that port is one of the first things the ROM does on power on/reset.
Based on the discussion in the other threads it kind of smells like your BASIC ROMs might be dead or non-functional, although I'm still not sure what to think about those black areas in the power-on photo. Maybe there's something broken with the timing chain and the CPU isn't even running, although I'm not sure why reset would change things...