MacBook Air crashes/powers down each time it's turned on.

I replaced OS 10.6.8 on my MacBook Air with Lion 10.7 when Lion became available last week.

Last night I noticed some odd behavior -- extremely slow "genii" minimization of screens, duplications of key strokes, and other anomalies.

Then today, each time I tried to boot up, as soon as the wheel stopped spinning and the desktop became visible:

1. Several windows automatically displayed -- windows I was working on when I shutdown earlier.
2. The dialogue box appeared with buttons for | Restart | Sleep | Cancel | Shutdown |
3. Almost immediately, the power cut off and the screen went dark.

"Reopen windows when logging back in" was checked, so I unchecked it. As a result, the Air now powers down without displaying windows or the dialogue box. It goes black almost as soon as the Apple logo and login wheel disappear. (I'm connected to the Power Adapter, so there's no problem about power.)

I tried several remedies that have worked in the past with OS 10.6+, but they're not working now --

1. Opening in Safe Mode: the system powered down while I was logging in.
2. Using Command-R to invoke Disk Utility: The system crashed before I could start Disk Utility.
3. Resetting my Power Management using the Shift-Control-Option + Power. The air powered down as soon as I turned it on.

Finally, I tried reinstalling Snow Leopard using the Install stick that came with the Air, but the system died before I could initiate a new install. What's going on?

First clue: I tried the fix-errors command, fsck, in single-user mode. It logged into command line fine, bu tbefore I could invoke /sbin/ fsck -fy as usual, a line appeared

: / root# AppleMCP89TMSpowerGatingdown(0)done

and the system died. Did something actually "power-gate down"? What's that mean? (MCP89 is an Nvidia video chip.)

Second clue: When I disconnected the Air's Power Adapter because of a lightning storm outside, the Air rebooted and then died, rebooted and died, etc. (I'm typing these comments on my Pro, of course.) It only stopped when I shut the lid.

Thanks very much for your knowledge, expertise, and suggestions for how to restore my Air or if it's a hardware problem, how bad it might be.