By accident, I just now restored an ADM3 (not the "A")!
Lowercase ROM was made with an pin-rearranged 2706 EPROM.
Additional RAM was inserted, DIP switches were set: works perfectly.
However, with lowercase ROM installed and DIP switches set, but extra
RAM missing,
the Space "0x20" was displayed as a " ` ".
So I think you have an RAM issue.
Perhaps cleaning the socketed extra RAM helps?
Joerg
  On Tue, Dec 13, 2016 at 5:50 PM, Steve Hatle
<shatle at nfldinet.com> wrote:
  I acquired an ADM3-A a while back from the NWA
auction, and a
 generous friend was able to get me the lower case ROM chip that
 was "missing"  from my terminal.
 I set the DIP switches and installed the ROM. When I turned on the
 terminal, the whole screen was filled with "`" characters before the
 host was ever started.
 When I started up the connected Sun machine, the terminal did display
 both upper and lower case characters, but the "`" characters remained
 and appeared to fill out each new line, and text printed out by the
 machine was followed by garbage characters - like "Login:nzzzz". Typed
 characters were correctly upper or lower as typed.
 I removed the ROM and cleaned the legs of the chip. I didn't clean the
 socket, since I didn't have anything like DeOxit handy. I did remove and
 re-insert the ROM a couple of times.
 When I removed the ROM and set the DIPs back to the original setting,
 the terminal worked like normal in all upper case. Setting the DIPs to
 force upper case, etc. when the ROM was in always showed the bad
 behavior though the characters were upper/lower as you would expect from
 the switch settings.
 TL;DR - bad and extra characters when the ROM chip is in, everything OK
 when it's out.
 So, barring a bad connection to the chip while it's in the socket, it
 seems like the ROM itself could be bad. I'll dig through the maint
 manuals and see if I can find anything related to this behavior. In the
 meantime, any ideas from the collective are welcome.
 
 Take a look at the silk screen on the board - ISTR there's another chip
 that needs to be added, some simple TTL logic.  I converted mine several
 years ago without problems - but that was with the original ROM.