I got it working! I commented out
if (Ethernet.begin(mac) == 0) {
Serial.println("Failed to configure Ethernet using DHCP");
// no point in carrying on, so do nothing forevermore:
for(;;)
Serial.println("infinite loop!");
delay(1000);
in sendTweet() and that solved it. That statement was in the wrong place anyway. Thanks for all your help!