MacBook Pro 13" Early 2011 - Internal keyboard and trackpad stopped working

This problem has been going on for a while, and I've tried everything I can think of, including chatting with Apple Support three times.

Here's the story. About a year ago, there was a mishap with some water that killed the machine. I took it to the local Apple Store, and they replaced almost everything that could be replaced aside from the actual hard drive. I replaced the hard drive myself, after the current situation began happening, because I suspected the five year old hard drive that had been in the machine (the one it shipped with in 2011) was failing. I think I was right, but that's besides the point. Really, I just say this to indicate to you all that most of the parts are new as of last year. The hard drive I'm using at the moment is lightly used, cannibalized from an older machine.

So, about a month ago, I was watching some TV show or other, using Flash video, and my display, keyboard, and trackpad all went dark and unresponsive. I ended up shutting the machine down by holding the power button. I had to try several times to get it to turn back on, because the display didn't want to cooperate. Finally, it did, but the keyboard and trackpad were still unresponsive. I located a USB keyboard and mouse and started investigating. About two weeks after that, I went to move my laptop to the next room to print something, and when I put the USB keyboard on top of the built in keyboard, it was working. So was the trackpad. No idea how or why.

About five days after THAT, the onboard keyboard and trackpad both went unresponsive again, this time after a routine reboot, and it hasn't come back to life yet. Since I can't be sure what happened to cause the initial problem, I obviously can't be sure whether it will resolve itself again, but there you go.

Interestingly, the keyboard works just after I power on the machine. I can boot into safe mode, press option to show a list of available disks, etc. But once it gets to a login screen, it's totally unresponsive. The trackpad doesn't have this quirk.

What I've tried so far:

- PRAM/NVRAM reset and SMC reset (several times)

- Two full OS X reinstalls; on the first, I upgraded to El Capitan, which is what had been my OS when this started, and on the second, I've got Yosemite

- Safe boot

- Disconnecting and reconnecting both keyboard and trackpad

- Removing the battery

- Taping down the trackpad ribbon (this was suggested on a number of forums; I saw no difference)

- Booting into a Linux live USB (when selecting a boot option from a textual menu, keyboard worked; after booting to the selected option, it was unresponsive)

- Apple Hardware Test (showed errors on the old hard drive; no errors found since replacing it)

- Checking System Preferences Keyboard and Trackpad panes - the trackpad seems not to be found at all; the keyboard has an option (Use the F1, F2 keys as standard function keys) that blinks, disappears and reappears, over and over and over. The Trackpad pane lists no onboard trackpad, but the Mouse pane has some blinking happening as well.

- Booted into verbose mode and checked Console app. This output repeats over and over, in both cases:

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDebug: _getFeatureReportInfo returned an error in AppleUSBMultitouchDriver::_deviceGetReportWithLookUp

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned with result 0xe000404f - retrying (reportID 0xd0)

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned error 0xe00002ed (interface 1, reportID 0xd0)

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDebug: _getFeatureReportInfo returned an error in AppleUSBMultitouchDriver::_deviceGetReportWithLookUp

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned with result 0xe000404f - retrying (reportID 0xa1)

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned error 0xe00002ed (interface 1, reportID 0xa1)

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDebug: _getFeatureReportInfo returned an error in AppleUSBMultitouchDriver::_deviceGetReportWithLookUp

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned with result 0xe000404f - retrying (reportID 0xd9)

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned error 0xe00002ed (interface 1, reportID 0xd9)

3/5/16 1:51:34.000 AM kernel[0] AppleUSBMultitouchDebug: _getFeatureReportInfo returned an error in AppleUSBMultitouchDriver::_deviceGetReportWithLookUp

3/5/16 1:51:35.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned with result 0xe000404f - retrying (reportID 0xd1)

3/5/16 1:51:35.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned error 0xe00002ed (interface 1, reportID 0xd1)

3/5/16 1:51:35.000 AM kernel[0] AppleUSBMultitouchDebug: _getFeatureReportInfo returned an error in AppleUSBMultitouchDriver::_deviceGetReportWithLookUp

3/5/16 1:51:35.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned with result 0xe000404f - retrying (reportID 0xd3)

3/5/16 1:51:35.000 AM kernel[0] AppleUSBMultitouchDriver::_getFeatureReportInfo - DeviceRequest returned error 0xe00002ed (interface 1, reportID 0xd3)

I know this is a lot of information, but I include it to be absolutely sure that if anyone has answers for me, they know not to suggest I try something like checking the battery for ballooning. I've been at this for some time now and have tried literally everything I can think of. I appreciate any insight anyone can offer.

EDIT: Forgot to mention, the keyboard backlight does work. I have it set to turn off after five seconds of inactivity, which it does, for a second. Then it comes right back on, even if I'm not touching the machine at all.