Old topic but maybe i'm not the only one to still try to fix a MBP 2010... My keyboard has the LEFT SHIFT key permanently enabled due to liquid ingress, which forces startup without extensions. Here is a workaround if you can't replace your keyboard: - if you press the LEFT CTRL key during the early stage of startup, it will cancel the effect of other stuck keys such as mine, and allow normal startup. - then, you can use a Freeware called Karabiner to disable the failing key (you can also setup an alias key if needed). On my side I received a replacement keyboard and will soon try to install it, now that my MBP with failing GPU does not crash anymore thanks to this thread: https://forums.macrumors.com/threads/gpu-kernel-panic-in-mid-2010-whats-the-best-fix.1890097/
It seems that the antennas are integrated inside the back plastic cover (the one you need to unscrew to access the battery), and is connected to the mother & daughter boards via spring contacts. You may try to clean those spring contacts using alcohool, maybe they are dirty following the spillage... I'll give a try tomorrow with mine (left at work)
I confirm Etain's solution: the pill blister trick works perfectly for power & volume buttons. You can try without opening the phone but the best way is to open it (only 8 screws!), so you can position precisely the pill-blister and even secure it to the case using a bit of adhesive tape. My Lumia 520 works like a champ since I fixed it this way months ago. Go to youtube for tutorials!