Initially, I was planning on using a HELOC with the equity in my personal home to purchase this property, do a few minor updates like new carpet and paint and turn around and sell it within 30 days for 10k over what I paid.

The lenders allow clean up, some painting or even carpet replacement.

You are looking to paint and carpet only... $10 per sf = $27k. 

Homes similar have sold 114,000-120,000Owner says need new carpet and to pay off new a/c unit $5400 Loan and a few other repairsHe’s asking $109,000Could rent for 900-1000Is this a bad deal?

The home needs Painting, Windows, Carpet, and a new Kitchen.

For example a newer home will likely have less expenses than a home built in the 1920's, homes with carpet will in the long run be more costly than those with tile/laminate, and brick construction is darn near invincible ect. 

@Brad Carrier be careful not to over upgrade your rental, you can look at other rentals that are on the market to see what's necessaryFor example:You probably don't need granite countertops for a $550 rentalYour flooring should be either easy to clean (hard surfaces like tile or sealed wood) or easy to replace (carpet)

Ughhh - we're replacing carpet and painting.

The property could have used carpeting (which has since been completed) and a fresh coat of paint on the walls would have helped, but at the time, I just needed some additional cash from the property as it was free and clear at the time (now has a 37k lien on it). 

If the unit is not carpeted, spring for a Rug Buddy heater.