To let a fine automobile like an E92 with just 137,000 miles on it to sit for 2 years and then SCRAP IT, is automotive blasphemy, let alone a case of BMW abuse. A well cared for E9X at 137,000 miles has literally hundreds of thousands of miles left in it. Why didn't he just sell it when it was in drivable shape. It says the current owner really didn't care for the car before he parked it to let it die. So I'd offer him very little money for it (he was going to scrap it anyway), since you really don't know the level of abuse the car has seen due to lack of proper maintenance.
So a bit more about rodent damage. I live in a rural area and have several cars that sit for mere days or at most a week, and every one has had rodents move in and cause damage. From 2004 thru 2017 I had two beagles, who freely hunted my property for hours every day, and there are plenty of snakes, birds or prey, and other "hunters" to keep rodents at bay, and even my daily driver, which sees 170 miles a day, still got attacked by mice (George will remember my comment about "killing the mouse" from a few years ago
).
So what I would do is remove the cabin airfilter housing (people mistakenly call it the "cowl"). It takes just a 8MM socket and 5 minutes. You will get a better look at the wiring harnesses up on the firewall. And more light will allow you to look at the starter between the intake runners. There is a single "signal" wire that triggers the starter solenoid, which if broken, will cause the problem you are experiencing. The engine in the E9X is canted to the right, about 15 degrees, which creates a perfect ledge under the intake manifold for a rodent to make a nest on the left-side of the engine block; I found a nest there in my 325i when I replaced the starter/CCV system last year, and several other members here have found nests as well. The signal wire for the starter hangs freely in space right where rodents like to make a nest on the engine in an E90.
Remove the cabin airfilter housing and get a bright flashlight and verify the signal wire is still intact as a first order of diagnosis. You need to look between the 5th and 6th cylinder intake runners to get a good look at the starter, which requires removal of the cabin airfilter. If you find the wire intact, then I really think the starter went bad sitting for 2 years. The Bendix-drive that throws the starter gear onto the flywheel ring gear eventually gets gunked up with dirt and will stick, which is why hitting the starter while it is energized sometimes frees the Bendix-Drive and the starter works again. Letting the starter sit make the problem worse. Hell, it might be worth trying to get some penetrating oil on the starter in the hopes it creeps into the Bendix-drive.