YOu don't need that exact chain ring. 36T, 104 BCD
If it was me, I'd drop a new cassette and chain on it.
New chain, cassette, and chain ring you'll be under $50, peace of mind - Priceless.
Cassette tool, allen wrenches, chain tool, chain whip. Bike Co op nearby to assist and use tools?
https://www.jensonusa.com/Shimano-De...PEED-Chainring
https://www.jensonusa.com/Shimano-CS...Speed-Cassette