I reset the SMC and now it has a looping chime

My wife's 2011 MacBook Air 13" slowly had the keyboard and trackpad become less and less responsive until pretty much only an external mouse and keyboard worked. She seemed to be getting along fine but recently asked me to actually fix this. When she had taken it to Apple they said there may be corrosion on the ribbon cable connections. This sounded possible but before opening it I thought I would so some basic PRAM and SMC resets. Much to my chagrin after resetting the SMC it's now in a constant boot chime loop. The screen comes on, it chimes, then it probably chimes every 3 seconds until I hold the power button and turn it off. I've done a bit of research but there doesn't seem to be many solutions. I don't have an external drive with a Mac OS to try and boot from and the loops is so fast I can't even try resetting PRAM again. I never even got to resetting the PRAM because I did the SMC reset first. It seems one person solved this by replacing the flash memory on the board. This was on this site but I haven't gotten a response as to what he's talking about. He implied it wasn't the SSD but his English wasn't very good so I'm not sure what he's talking about beyond that. I've seen some things about an Amtel chip that stores the Apple equivalent of a BIOS setup and serial, etc. Supposedly you could replace or reflash that with a fresh setup since things seem to point to that being corrupted. The thing is it's soldered to the board and there doesn't seem be an easy to replace or refresh/reflash this. Any suggestions or narrowing down of the above? I may take it to the Genius Bar just to see what they say since my issue has changed from what it was originally. I'm wondering at this point if a complete logic board change might be better, but not sure I'm willing to invest that much. Thanks for all of your help!