We propose a classifier that can identify ten common home network problems based on the raw textual output of networking tools such as ping, dig, and ip. Our deep learning model uses an encoder-only transformer architecture with a particular pre-tokenizer that we propose for splitting the tool output into token sequences. The use of transformers distinguishes our approach from related work on network problem classification, which still primarily relies on non-deep-learning methods. Our model achieves high accuracy in our experiments, demonstrating the high potential of transformer-based problem classification for the home network.