Car won't start when cold

When it's cold, like below 40, my hybrid system won't start. It beeps and the lights come on, but the ready never lights up. I bought the car 2 months ago used with 64,000 miles. I have found if I left the defrost on from the last time I ran the vehicle, it takes longer to get the car to start next time. This seems odd. Is there something special that needs to be done in order for the car to start when it's cold out. From what I've read from other posts on this site, I need to check the 12 volt battery. I have a friend who's going to check that for me tonight. What is the best way to check it? If I check if after I drive about 1/4 mile to his place, will that be a problem or shall I have him come to me to check it? He has one of the voltage checkers. Where is the battery I need to have him check and what numbers indicate it needs replaced? Is there somewhere other than Toyota that I can get the battery? I don't trust the Toyota dealership nearest me after what they pulled with my old Camry. I've had this same problem with it not starting in the past when it was cold in the mornings and at night and after turning the car on and off enough times eventually it will start the hybrid system, but today I was late to work because I finally had to give up and walk because it was taking so long and I had an appointment at 9:30 which I was late for. This cannot keep happening. The past week or 2 when I put my foot on the brake and hit power, the lights power on and then I have to hit power again and the hybrid system clicks on. I really hope it's not the hybrid system...

 

I just ordered a Optima yellow top as recommended in other threads. I didn't have time to do the usual pushing of the button a bunch of times like I have in the past this morning, but can plan ahead better for the next few mornings and get through until the new one arrives.

 

Update, the new battery fixed this problem even through a winter of extreme cold.