If it beeps on startup instead of booting, then you have a dying logic board that is common on these old 2011 MBAs. In that case, there is not a lot you can do, besides disassemble it and sell it for parts. Otherwise these laptops usually benefit from complete system format and reinstall and thermal paste cleanup / reapplication. Other than that, worn out batteries may cause it to slow down to prevent unexpected shutdowns if used on battery, and once or twice the cause for a very slow machine was a dying SSD. Trackpad button can be cleaned, but it is a nuisance and I don’t think there is any guide showing how to do it.

Most likely a logic board issue. You can try disconnecting the battery and try it without it

There where: (1) A1369 MacBook Air 13’’ Late 2010 and Mid 2011 - they use the same SSD format although the 2010 & 2011 are SATA based Vs PCIe/NVMe (2) A1466 MacBook Air 13’’ Mid 2012 - they used special SSDs that are compatible only with 2012 models (3) A1466 MacBook Air 13’’ Mid 2013, Early 2014, Early 2015 and 2017 use the same PCIe/NVMe based SSDs, with the 2015 and 2017 being faster, but they are interchangeable (4 lane Vs 2 lane)

You have a short to ground (chassis) somewhere. Could be number of things, most likely a worn insulation on a cable that now has exposed bare wiring and is touching to the car frame.

I had a similar problem on a iPhone 7. Turned out to be bad logic board, specifically the charging IC. The phone drew current until it booted, then it stopped.

You can do a swap if you wish. And it should work, because you will be essentially changing the whole phone sans the case and ancillary components. But remember the TouchID won’t work. And I heard that some second boards could have other problems you cannot expect. I wouldn’t risk it.

This is a 10+ year old laptop which doesn’t support MacOS Sierra or newer. Even El Capitan is not necessary supported. Most likely you would be stuck to Lion or even perhaps a Snow Leopard if you are dealing with the first gen A1181. You are getting no entry sign, as the laptop tries to boot into MacOS it is not supported on this machine. Internet recovery was not a thing on these laptops, and only Late 2009/ Mid 2010 and newer support it. So no Cmd+R or any other recovery methods besides the physical installation media. Your best bet is to get a Snow Leopard Installation DVD, or a Lion Installation USB Stick (this one could be created from the working machine, but you must also obtain the installation image). Or use a Recovery DVDs that the laptop came with. Then you can boot to installer, format the drive and do a fresh install of the OS X.

Usually the AC adapter fails on these machines. In fact, I haven’t seen an AC adapter in the last 5-7 years from these series PowerBooks that was still good. But luckily, they are easily repairable, just need a complete replacement of capacitors. I repaired two in last year and they now work as good as new. So, replace or repair your AC adapter (7.5V 2A) and see if anything changes. If you have a voltmeter nearby, check the output voltage on the adapter output jack.

Was your logic board recapped properly? If not, then do that first, and also clean the PCB very throughly before you solder the new capacitors. They used a type of capacitors on these machines that are prone to leaking and shorting out the logic board after 15-25 years or so. Otherwise, it is also very likely a logic board problem, more exactly it could be a Bourns filter problem. So that needs to be replaced. As the Larry Pina in the book The Dead Mac Scrolls says: "Symptoms: On startup, the desktop appears, but neither thekeyboard nor the mouse work. Typical history: The problem occurred when you connected ordisconnected an ADB device while the computer was on. Probable diagnosis: The problem is on the Mac SE logic board. Solution: Check/replace the shorted fiIter (Apple part 155-0007-E) at board location A 11"

If you follow the official service manual that can be found with some googling, then why not. I’ve done it a few times myself on these machines with no problem. The only major risk is breaking the CRT on the neck itself if you don’t remove the neck board (just pulls straight). Most likely, the floppy drive itself is not broken, just in need of some overdue service, like some lubrication and head cleaning.