Dryer is new, uses 3 prong outlet from old dryer. been working for over a month. Now, the motor works but no heat. However, the real puzzle is that when I turn it off, the oven, the fridge, the ceiling fan and outlet in the kitchen shut off, as do the lights in the basement and the furnace fan. The outlets in the rest of the house work fine. There appear to be no circuit breakers blown. One last clue, it seems there is some minimal power in some (maybe all) of the lines... the computer shut off, tried to start and continued to shut off before booting and the light in the microwave in on, but when I attempted to heat something, it simply exhibited a grunt and shut down.
Call the power company NOW and report a power outage!
You lost a leg of your power connection. Your power is literally out. Don't run any 240V appliances until it's fixed.
The 120V loads in one-half of your panel will still work, this will be every other row in your breaker panel, so spaces 1-2, 5-6, 9-10 etc. (or NOT those spaces).
You are rather lucky. There was a 1 in 3 chance of having lost the neutral. If you had lost the neutral, with that hokey old 3-prong dryer connection, it could have electrified the dryer's chassis and killed you. That's because the dryer punched down for 3-wire bootlegs ground, using neutral as ground, so when neutral fails, your ground becomes dangerous. Now maybe your panel's neutral-ground bond would've saved you, but I tend to trust nothing in obsolete electrical systems e.g. those with 3-prong dryer connections.
If this is the only device in the house having issues it may be in your panel not the power company's issue. If you have an electric range is the oven working? The circuit that has problems is it an even or odd breaker, turn it off, and check if there are any other circuits that are on the same leg having issues All would be even or odd in most cases depending on the panel. If this is only an issue on 1 circuit or possibly a multi wire branch circuit the neutral is probably open , if there are multiple circuits that have the issue call the power company, turn off, unplug devices or they may get fried.