Car intermittently won't start, sometimes dies when accelerating from slow speed or stop

My family has had this car for a long time. It worked fine for years but in the past year it has had some problems when starting. Sometimes the car starts fine, sometimes it won’t start until you re-try a few times, sometimes it won’t start and you can try over and over and it never does. When it doesn’t start, it doesn’t do anything at all, no sound or anything. The battery is not dead, the car has more than half a tank of gas. Recently, the car started fine, but after driving it for a while, we stopped at a stop light. When we tried to accelerate after the stop, the car died, during the acceleration and a left turn. We got the car going again after trying a few times, but later that same trip, the car died again when accelerating, but this time it was from a slow speed, not a stop and it was while we were driving straight. The car is well taken care of (oil changes, check the oil, do not let it get to under a quarter of a tank, change transmission filter & oil, air filter, brakes, etc.) The timing chain is permanent, stainless steel. We do not drive very much but we are afraid to now that we don’t know if it will die while we are driving. Please help! Thanks!

PS We fix our car problems ourselves just fine normally, and we do not like to put our cars in the shop because of price, time, etc. so anything that we can do to fix this ourselves would be great.

I would start off by checking both battery cables making sure the contact surfaces are all clean and securely fastened. Same with the wires to the starter, while you are at it.

You might want to start by measuring the voltage at the battery and at each end of each cable.

Thanks for your advice, I really appreciate it. We already tried those things and they did not fix the problems, so I am hoping that there are some other ideas out there.
thanks again!