I've just tested TP's faucet and it worked (green success text).
Are you sending to a testnet address (begins with m, n, or 2)? I'm thinking you may be inadvertently using Mainnet or Regtest mode (beginning with 1 or 3).
Ensure your Bitcoin.conf file has
testnet=1 in it, or use the
-testnet flag on the command line. Also be certain your blockchain is fully synched (this will take many hours, unlike regtest mode)
Go into BitcoinCore's client, and try
getnewaddress in the console (help > console). Then copy/paste that address into the faucet, complete the CAPTCHA, and the coins will have been sent. You will need to have a completely synched blockchain before the coins will "appear".