You missed my question: how much memory is displayed on the boot screen? the usual 3583 bytes free, or less? If you read less than 3583 bytes free, than you probably have a ram issue.
Are your two VIC the same revision? If yes, you could plan to swap ram chips.
There are two kind of VIC; an early revision with lots of ram chip (2114 if I'm right) and a later, most common revision with just two 6116 ram chip at UI4 and UI5 (two 24 pins ICs at the bottom left corner, under the two 6522 via chips.
In this latest revision there are also three 2114 ram chips, UD2, UE2, UE1 (at the right of the 6116 ram chip) used as video ram, but they should be the culprits.
However, before warming you iron solder ;-), we can write a very little program to check your memory. I'm sure there is a better and more elegant test based on poke and peek, but since I don't remember almost anything about 1980s and VIC (too much beer and whiskey and hot girls in those years ;-) ), try to type this little program. It makes an incremental use of variables, consuming all the free ram (that's very easy with VIC

)
10 N=0

RINT"{clr}" << instead of {clr} you should type shift + clr/home, it will appear a negative heart.
15 DIM A$(100)
20 FOR I=1 TO 100
30 A$(I)=""
40 NEXT I
45 N=N+1
50 FOR I=1 TO 100
60 A$(I)=A$(I)+"X"
70 PRINT "{home}";N;" ";I;" " << instead of {home} simply press the clr/home key, it will appears a negative "S"
80 NEXT I
90 PRINT "{cursor down}";A$(1)
95 GOTO 45
This program declare a 100 alphanumeric cells array, and then makes an incremental declaration for every cell. I used array because I don't remember the size limit for a single variable.
then type RUN and see what happens. You will see some numbers running in the first line of the screen and some "X" in the next line.
At the beginning program will run fast, but it will slow down as the A$ array getting bigger.
The Xs represent the length of every A$ array cell.
If you typed this program exactly as I did, you should get an out of memory when the numbers in the first line are: 31 61; this is what I get on my working VIC. If you get an out of memory with lower values, than you have a ram problem. At least I believe that!
-- Giovi