Hello I will help you with your question,
The starter requires the battery to provide a lot of current to spin the engine so if you have a weak battery or corroded battery cables the starter will sap the battery causing the dash lights to flicker and the other symptoms you are experiencing. Either the starter (not likely) is drawing too much current or the battery is weak and has enough charge to run the radio and light but not enough to run the starter (more likely). or the cables have corrosion on their ends or are loose. If the cables are clean and tight have the battery checked for free at an autoparts store and let m e know the findings. I believe you need a battery but have it tested first.
Let me know how I can help