Final answer:
The song with the described synth riff is "Blue Monday" by New Order, a standout synth track from the early 80s that fits the timeframe and genre described.
Step-by-step explanation:
The song you're describing with the synth riff that goes "do doot do doot do doot do do, do doot do doot doo doo" is likely "Blue Monday" by New Order. This track is famous for its distinctive, synthesizer-driven hooks and was released in 1983, making it a match for your description of late 80s/early 90s synth music, possibly rock. It's not "Sweet Child o' Mine" by Guns N' Roses, "Take on Me" by A-ha, or "Every Breath You Take" by The Police as these songs have different, distinctive intros that don't match your description.