Power steering dies, not all power gone won't restart

check and test battery ---have vehicle scanned for codes --check connections under dash [you have elect motor assist power steering mounted on steering column under dash

I am assuming you mean you loose power steering when the steering wheel locks up, which would be a normal event if the engine dies. Same goes for the battery light since the alternator would stop charging the battery.
Someone will need to figure out if you are loosing fuel or spark when the engine dies, then troubleshoot the problem. It may be difficult to find if the mechanic can not duplicate the problem in the shop.

The battery ran out of power because the alternator is not charging it.
Have the alternator output tested and take a look at the fuses.

If the engine died you would loose power assist steering and power assist brakes. I have to think it was an electrical power failure somewhere.
Will it start up and idle now ?

Sounds like belt is missing. If gone the altenater wont charge the battery back up so it just sucks the power out of it when running.

LOL, nooooooo. You didn't hurt anything. In fact, you identified a problem by going through that puddle. You need a new serpentine belt and/or tensioner pulley. It sounds like the spring in your tensioner pulley may be worn, and not pulling your serpentine belt tight enough. Now, THAT being said, there MAY be yet another issue going on. While I don't doubt for a minute that you need 1) a new serp. belt, 2) a new tensioner pulley, and 3) a can of belt dressing, you may also want to check (while the old serp belt is off during the changing) that all your pulleys are spinning freely. Especially your AC compressor pulley. If your AC is low on refridgerant, it can lock up the pulley. The serp belt drives your power steering pump, your alternator, your AC pump, water pump, etc. If one pulley siezes up, the tensioner is weak, and the belt gets wet, NOTHING will turn. Hence the dead battery (alternator not turning), no power steering (pump not turning), and more importantly no coolant circulation (water pump not turning), which can cause serious overheating problems.

you have a faulty alternater there is a speed sensor in the alternator that is linked to the power steering if the alternater isnt charging the steering wont work either replace the alternater and all should be ok

sound like alternator.

either your alternator has gone or your fan belt is not there which helps the alternator to charge the battery get a volt meter on your alternator to see if it is kicking out what it should be