When every reading is nan

Start from what it prints

There is nothing else to go on. The DHT11 has no way to say "I am here but you asked too soon". Either forty valid bits arrive or they do not, and everything else is inference from what the sketch prints.

The order to check in

First, the sensor type. It is one line in the sketch, it is never detected, and it causes the two commonest symptoms: silence, when the DHT11 is declared as a DHT22 and never wakes, and numbers in the hundreds, when it wakes anyway and is decoded as one. The TK38 is DHT11.

Then the pin count. Count from the square pad: GND, VCC, NC, DATA. The third pin is connected to nothing, so wiring by position and being one out leaves DATA on a dead pad, which looks exactly like a dead sensor.

Then the supply. Is VCC on a rail that is powered, and is it the voltage your pins expect? A DHT11 with no supply is silent. One on the wrong supply usually works, and quietly stresses the input pin.

Then the timing. A number that never changes is the library's two-second window or a room that has not moved a whole degree, not a stuck sensor.

Last, the placement. A reading two degrees high on correct wiring is not a fault: the sensor is telling you how warm your board is.

What nan is

readTemperature() and readHumidity() return NAN rather than an error code. It prints as nan, and it compares false against everything, itself included:

if (celsius == NAN)     // never true, ever
if (isnan(celsius))     // this one

That is the only check that works, and it is why every sketch in this book has it. A nan printed straight into a graph or a web page is how a wiring fault gets taken for a sensor reading zero.

When it fails now and then

An occasional failure is the protocol, not your build. The forty bits are measured by counting loop turns with interrupts off, and anything that disturbs the count, such as a slow edge on a long wire or a busy radio, turns one bit over and the checksum discards the frame.

Retry rather than report, and respect the DHT11's one-second floor between tries:

float t = dht.readTemperature();
for (int i = 0; i < 2 && isnan(t); i++) {
  delay(1000);                            // the DHT11's own minimum
  t = dht.readTemperature(false, true);   // force past the stored value
}

Two retries cover ordinary bad luck. If it needs them every time, look at the wiring and the placement rather than the code.