LastMinuteEngineers.com had a good writeup on this. I share the relevant piece below but the whole article is worth checking out. In-Depth: Send Receive SMS & Call with SIM800L GSM Module & Arduino
As @AndrewGifft mentioned the SIM800 could be damaged so if the problems persist after adding the resistors you may need to replace the cell module.
We cannot directly connect Rx pin on module to Arduino’s digital pin as Arduino Uno uses 5V GPIO whereas the SIM800L module uses 3.3V level logic and is NOT 5V tolerant . This means the Tx signal coming from the Arduino Uno must be stepped down to 3.3V so as not to damage the SIM800L module. There are several ways to do this but the easiest way is to use a simple resistor divider. A 10K resistor between SIM800L Rx and Arduino D2, and 20K between SIM800L Rx and GND would work fine.
