RX300 cold no start problem

[ukrkoz]

hello
99 RX300
brand new battery
tight alternator belt
it's about 11 degrees outside and it is parked outside overnight
starter will not kick in at all. it can take up to 10 attempts to turn key in the lock, then it will turn and start. let me clarify: key TURNS into the "start" position. starter does not come up.
all lights inside the car/instrument panel are good.
no warning lights of any nature.
no trouble codes.
i have to rely on my wife's description of this. per her, it simply does not cranck, then does it. happened about 3 weeks ago, i replaced battery. cought her yesterday and today nights. basically, security people come over and try to jump it, after she tries 3-4 times. she told me it will take several attempts to turn the key, even with jumpers connected, with no response from starter, then it will just turn and start.
if parked inside garage at home, none of this trouble, starts right away.
any suggestions? she works night shifts and that's her regular commuter.

[moeljo]

i think it's your starter or your p/n switch.

[ukrkoz]

oh my, i have totally forgotten about this post.
yes, it was starter.
thank you.

[holdercraftman]

Solved it?