I have the exact same problem, no warranty available, what did you do? i'm trying to fix it by my self but I don't know where to begin. So frustrating!!
Well, I opened the base up. No obvious signs of water damage, checked all connections. Cleaned with alcohol (though I didn't bother taking the discrete graphics out or trying to get into the keyboard). Not one key came back, so figure it was pretty kaput (I'm thinking I bought a charger from
Amazon that surged into the Surface and killed an IC or something...I will never buy or cheap out on the charger again if I paid thousands for a device).
Anyways, I was in the market for a new device, so after much tossing and turning, I got the SB2 15 inch. I really looked at Dell, Asus and Lenovo 2 -in-1's, but it was the GTX 1060 in the 15" in the small factor that did it for me. I hate that the SB 2 doesn't have Thunderbolt (for a proper docking solution), the charger is underpowered, doesn't seem to properly support HDR on external TVs, and there is no way to fix/upgrade things; but such is life.
If I was on a budget, I would have looked at the $600 out of warranty "trade in" (after backing up all my files, twice!...and checking I got them all) and get a swap (driving 3 hours to Charlotte because I don't trust them going into a bin and shipping me whatever). The problem is you only get a 90 day warranty...lots of risk as the reputation of 1st party refirbs hasn't been great lately (i.e. Apple). If my base was in perfect shape, I might have rolled the dice on getting the base from
Ebay, but what I saw there wasn't exactly cheap, and mostly looked like junk.
So at the end of the day, sadly, consumer laptops and computers have become commodities. Until MS decides to sell replacements for the base (I have a working SB 1 tablet...no base which is a shame), you're pretty much hosed. Or until Louis Rossman (look him up on YouTube on his Apple repairs and commentary...good insight) decides to fix Surfaces.