Latitude D620 RAM issue/question

I'll try to summarize my issue quickly...basically, got a Latitude D620, 32-bit, running Windows 10 Pro.  I'm pretty sure my DIMM B RAM slot (the one under the keyboard) has gone bad.  When I have a 2GB RAM module in there (and, yes, the RAM module is good, I've checked it), and also have a 2GB module in the DIMM A slot, the laptop won't boot up...the Cap Lock and Scroll Lock lights at top of the keyboard just blink on and off.   When I remove the RAM module from just the DIMM B slot and try to re-boot, it boots up fine with just the 2GB module in slot A.  

So, here are my main questions:

1) Does anyone know if this is a common problem with the DIMM B slot, is there possibly a solution to repair it or run a diagnostic to figure out if it is just a loose wire or something simple, or is that thing likely fried?

2) Being that my DIMM B slot isn't working, I'm running on only 2GB of RAM.  The laptop runs, but sluggishly.  I was hoping that I could just put a single, 4GB SODIMM DDR2 module into DIMM slot A to bring the laptop back up to 4GB, but from what I have found so far, both DIMM A and B can each only take (up to) a 2GB module, at most.  Is this true?  If not, I have found a few, single 4GB modules that would physically fit into DIMM A (like this one...https://www.amazon.com/Crucial-PC2-6400-200-Pin-Notebook-CT51264AC800/dp/B001RB21JE).   Would this work, or is that a no-go?  (And if anyone can maybe point me to a cheaper one, that would be great!)

Any other suggestions on how to get around this and get back up to 4GB RAM?

Thanks for any help.