Inability to start the car after no use for 5-6 or more days

I rarely use the car listed above vehicle (4 door), so I leave it parked for several days at a time before attempting to. I live in San Francisco where the temperatures in the last month or so have ranged from the 60's during the day to low 40's at night.
Beginning about 3-4 weeks ago, I found I was unable to start the car after it had been parked for5-6 days. I would then call AAA for a jump start and it would start up relatively easily. I'd then let it run for 20-30 minutes and, possibly, do some errands where I'd be able to turn off the engine in between doing 2-4 errand stops and restart the car with no difficulty.
I found I could always leave it 3 or 4 days without problems restarting but when it got to 5 or 6, I'd need a jump start. I had the battery, starter and voltage regulator checked by the company that sold me the battery. Their 'diagnosis' recommended 2 problems:
1)Replacing valve cover gasket and tube seals since they said oil was getting on the spark plugs (which they also wanted to replace). When I asked how the car could be easily jump-started without all the oil on the spark plugs being cleaned off, they had no answer. I am aware of the gasket problem but that it could cause the not starting up after 5-6 days of not use made no sense. One Toyota dealer agreed with me.
2)They said the Idle Air Control Valve was bad and needed replacement. As far as I'm concerned, I have never had problems with the car stalling and the car idles quietly at a low level. The same dealer I had spoken indirectly to (via a third party) believed that Idle Air Control Valve could be causing problems starting.
What wasn't answered is how could a jump-start cause it to start and then run smoothly with a 'bad' (possible dirty) Air Control Valve?
Your comments on the website 2 carpros. Com were that the air/fuel mixture could be thrown off so much as to prevent it from starting, though it was rare. Once again, why did a jump start cause it to start and run normally?
I don't know how the dealer who actually tested the car made his determinations, possibly by codes that showed up. I didn't trust his determination or thoroughness.
As a used car I seldom use for any more than local trips, I am reluctant to get a Toyota's dealer's diagnostic (about $225.00) and have them recommend repairs that won't fix my starting problem. I'm not convinced that the proper cause has yet been identified. I also will need to have the car smog-tested within a month in order to re-register it. Is there any mechanic you could recommend in the SF area?
Any advice would be appreciated.

Alan Steger