The NXT wallet includes pages which integrate with Shapeshift and Changelly.
In addition when funding your account for the first time the wallet will use the Shapeshift widget to exchange BTC to NXT.
However, the wallet uses the exchange APIs while the actual exchange is performed using Shapeshift or Changelly, therefore if something went wrong, please open support ticket for the relevant exchange and provide all the relevant information. From our experience they resolve tickets relatively quickly and efficiently and in most cases will simply refund your deposit to a refund address you'll provide.
Typical reasons for problems include:
1. Waiting too much time between getting the deposit address and making the deposit. This process has to complete within 5-10 minutes or else the exchange will cancel the offer and your deposit will never be exchanged.
2. Sending a deposit amount which is smaller than the minimum or larger than the maximum (with Shapeshift). Changelly has no maximum amount, however if you deposit a large amount of coins you may receive the withdrawal coin amount according to a very bad exchange rate.
Typically, any amount higher than 20 NXT and lower than 20000 NXT or the equivalent in the other coins should work and provide reasonable exchange rate.