As computing education becomes increasingly globalized, many students learn computer science through a second language. Prior work has documented cognitive and performance challenges faced by non-native English-speaking (NNES) students, yet less is known about how language background shapes their motivational experiences and intentions to persist. Drawing on Expectancy-Value Theory, we analyzed matched pre- and post-term survey data from 374 students (198 NNES, 176 NES) in a CS1 course at a large North American university. We measured programming self-efficacy, implicit theories of intelligence, need for cognition, sense of belonging, motivation and learning strategies, and intentions to major in computing. NNES students began the course believing intelligence is fixed and had lower self-efficacy on language-dependent tasks, gaps that persisted throughout the term. However, despite lower confidence, NNES students were more willing to choose challenging assignments and consistently used more strategic learning approaches. While NNES and native English-speaking (NES) students reported similar overall belonging, NNES students experienced greater belonging uncertainty, specifically when encountering difficulties, and were more likely to want to fade into the background within the CS community. These findings reveal language background as a persistent motivational cost in introductory computing and underscore the need for instructional designs that explicitly support belonging, self-efficacy, and adaptive strategy use for linguistically diverse learners.