Electrical – Flickering lights, sometimes no power to some

For the past few weeks some of our lights have occasionally flickered. Yesterday the power went out for those lights. At the circuit breaker box I didn't see any in the flipped position, but I went through them all, flipping each one off and back on, and when I was done, the lights were back on.

Today it went out again for those lights. This time I started by taking stock of what didn't have power, and saw that the oven, microwave, and garage door did not. But the oven clock was on even though the oven itself had no power. There is no battery for the oven clock. I thought that was strange.

While looking at the oven I turned the oven power switch off and on a couple times. Suddenly the lights went back on. The Microwave got power too. And then when I turned the oven off, the lights, and microwave display, went back off. I went back and forth like that several times. With the oven on, the lights and microwave display went on. With the oven off, the lights and microwave display went off. But always the oven clock stayed on.

It's a wall oven, wired into the wall wiring (not a plug). The house was built in 1962.

I recently had to replace the oven when the old one (very old, circa about 1980) died. That was maybe half a year ago. The new oven is a Magic Chef MCSWOE24S.

Any suggestions on troubleshooting? Any thoughts about what the problem is likely to be?

UPDATE:

Following advice given below, I called the power company this morning and they came by. They said they weren't sure what the problem was but replaced something that they suspected, referring to it as "old-style". They said to call them again if the problem kept happening and they'd put a volt meter on to monitor it.

I had previously unplugged the (over-the-range) microwave because it had triggered the problem a couple times. I plugged it back in and tested it and all seems well so far.

UPDATE 2:

Hours after they left, the power went out briefly, and later we saw lights flickering a couple times. So I doubt the saga is over yet.

UPDATE 3:

The problem is in the breaker box. A screw got loose and the connection has been burning up. If I can find an old used 1960s GE TRX2012S or TRX2012F box, the tech can replace the part. Otherwise $2,000+ for a new breaker box and getting up to code. Any idea where I can find that old breaker box?