Complex sentence: The band easily won the competition (and the bass gear) and also caught the eye of a young producer called Matt Elliss at Axis Studios who offered to record a demo at the studio free of charge.
Split into simpler sentences: The band easily won the competition and the bass gear and also caught the eye of a young producer called Matt Elliss at Axis Studios. They were asked if they wanted to record a demo at the studio free of charge.