Sounds like you're on the right direction here to at least finish diagnosing if the internal display connection is the issue or not.
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So you'll need a Mini-DVI (iMac) to HDMI (TV) adapter [https://www.bestbuy.com/site/j5create-mini-displayport-to-hdmi-adapter-white/8755801.p?skuId=8755801|j5create - Mini DisplayPort-to-HDMI Adapter - White] and HDMI cable.
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So you'll need a Mini-DVI (iMac) to HDMI (TV) adapter [https://www.bestbuy.com/site/j5create-mini-displayport-to-hdmi-adapter-white/8755801.p?skuId=8755801|BestBuy - j5create - Mini DisplayPort-to-HDMI Adapter - White] and HDMI cable.
Once you've got it connected up let us know if the problem persist. Good Luck!
Sounds like you're on the right direction here to at least finish diagnosing if the internal display connection is the issue or not.
So you'll need a Mini-DVI (iMac) to HDMI (TV) adapter [https://www.bestbuy.com/site/j5create-mini-displayport-to-hdmi-adapter-white/8755801.p?skuId=8755801|j5create - Mini DisplayPort-to-HDMI Adapter - White] and HDMI cable.
Once you've got it connected up let us know if the problem persist. Good Luck!