Could use some guidance Door locks, power steering issues

[new2330i]

Hi everyone, Great forum from what I see so far. I am hoping someone here can help me out. I recently purchased a 2001 330I from a lady and found some problems I am trying to correct.
1rst problem: Door locks will not work, via the key. I see a lot of threads regarding this and have tried re programming the key but to date no luck. I went to replace the battery and found out it recharges itself, which is ok, but also tested the key with their tester and I got the green light meaning my key is sending a signal. Right before I bought the car the lady had a new alternator and battery put in the car, could the lock control box need reprogramming by the factory becuase of the battery change? I have tryed my second key and I cannot get that one to work either. Also no trunk via the Key.
2nd problem: I live in New England and I am currently having intermintent power steering problems. It seems when the temp gets below freezing, the power steering acts up and does not work or works intemitently. I had a garage flush the system the best they could and put new fluid in it and it did help, but the problem is not solved. The belt is good, new pulley on power steering pump. Could there be moisture in the rack somehow?

Any help you folks could give me would be appreciated. I am welll versed mechanically, but do not know the BMW's yet. Thanks