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Hi, welcome to JA.
Thanks, XXXXX XXXXX trully do sound like a weak battery...even if all the other power accessories will operate, the engine starter requires the largest amount of amprage. I would remove the battery and have it tested at a local repair facility...or if you have AAA, they usually come to you to test the battery. Also, check the cables on the battery, if they're loose or heavily corroded, the same symptoms will occur.
It would be a starter if you told me you heard a clicking noise..but since the lightls flicker...it REALLY sounds like a battery or loose cables. But let's say it is a starter your looking at about $300 for parts and labor to put one in. I don't normally see bad starters at this milage. BTW, be sure you get the correct battery...most places don't sell this exact size, and they tend to sell something else that MAY fit but usually is a headach to get in there. The battery is under the cowl cover, below the windsheild...there is a smaller access hole with the + and - signs on it.
No problem...Happy Holidays :)