RAM slot dead - MBP 15 Mid 2010

Question

Hi guys,
I was away from home for a week and my MBP was turned off for the whole time.
As I got home and turned it on, not even 5 minutes had passed while I was checking my email and it rebooted on its own out of the blue.
Problem is it wouldn't restart. and had 3 beeps going with the let and screen off.
After some digging on the web I get that it's a RAM problem.
I was working with 2x4GB sticks for about 3 years now. Zero problems so far.
So I first opened it up, removed both sticks, cleaned the slots and the sticks and restarted - No success (3 beeps)
Then I removed my outer RAM stick (1x4GB) and restarted - Restart was a success! no problem at all
Then I did the opposite and removed the inner RAM stick (same stick as before) and used just the outer one - No success (3 beeps)
So then, I did the exact thing again with the other 4GB stick I have, and the results were the same.
So I gather that my inner slot works on its own, but if I use the outer slot with it or alone, I get the 3 beeps and no reboot.
So here is the real question: Can I use a single 8GB stick and use it on the only working slot I have? Will the MBP work like this?
Because I really don't want to have the logic board replaced if I can use the full capacity of RAM that I need.
In the off event that I do need my logic board replaced, can I upgrade it in the process? If so, to which specs?
In case you need it, here go my MBP specs:
Model Name: MacBook Pro
Model Identifier: MacBookPro6,2
Processor Name: Intel Core i5
Processor Speed: 2,53 GHz
Number of Processors: 1
Total Number of Cores: 2
L2 Cache (per Core): 256 KB
L3 Cache: 3 MB
Memory: 4 GB
Processor Interconnect Speed: 4.8 GT/s
Boot ROM Version: MBP61.0057.B0F
SMC Version (system): 1.58f17
Serial Number (system): W80202B3AGV
Hardware UUID: 8BE69D4E-5035-57C8-B670-C7A60F1AA668
Many thanks for your help in advance!

Answer 1

So here is the real question: Can I use a single 8GB stick and use it on the only working slot I have? Will the MBP work like this?
Doubtful. You can definitely run one 4GB DIMM.
Before you give up, there are anecdotes that the machine in the factory that tightened the bolts on the slot adapter sometimes made them too tight. Remove your DIMMs and try loosening the bolts on the memory slot adapter until they are loose, then tightening them "just snug". Then re-insert your DIMMs and try again.