He was on the 1958 team that brought the Colts what was then the league's most-coveted prize: the NFL championship.
But just as the Liberty-Garrison neighborhood where he ran a liquor store for 35 years has lost some of its vitality, so has the man nicknamed "Unitas' Protector" for the pass protection he provided quarterback Johnny Unitas.
Today, Parker, 65, takes several seconds to rise from a chair. He is diabetic. He has had at least one stroke. And he uses the blue wheelchair in front of his Columbia home to travel to the steps at the edge of his driveway. He closed his liquor store two weeks ago, but instead of relaxing, he struggles with do's and don'ts.
Although he's not supposed to smoke, he seemed happiest during a recent interview when he lighted his pipe.
Drinking also is taboo. He insists the Hennessey, Smirnoff and other spirits at the bar in his home are for friends. Yet, after pausing for a moment, Parker acknowledges drinking a 22-ounce Heineken "every now and then."
His favorite food is ribs, and although doctors forbid him from eating them, he acknowledges devouring some once a week, much the way he brags about how he used to eat up Deacon Jones, one of his toughest opponents.
Long removed from the game but not the glory, he fondly recalls the battles that made him a household name.
As he prepared to leave the game, he worked briefly for a liquor distributor and had such success his boss helped him buy his business in 1964 when the neighborhood in Northwest Baltimore was thriving.
Predominantly Jewish in the 1950s, the neighborhood boasted a Union Trust Co., Silber's Bakery, Shure's Pharmacy and The Forest Theater, among other businesses.
But as has been evidenced in many areas of Baltimore, the population was pushed to the suburbs by encroaching crime and drugs, and businesses began to fade.
So did Parker's health, forcing him into retirement.
'He gets evasive'
His children are glad he gave up the store, as is Colts great Lenny Moore. Moore said it wasn't hard to recognize during phone calls and visits last year that something was wrong with his former teammate and fellow Hall of Famer.
"He looked kind of out of it," Moore said. "I'd say, 'Hey, man, what's wrong with you?' Then he'd say 'Oh, I'm all right.'"
Moore knew Parker was being macho. After all, Parker had played football in the '50s and '60s, when the game had no official disabled player lists.
"I know he gets evasive," Moore said. "With Parker, he may just say something to get you off the subject. I know him. That's why I know exactly what to say and how to say it."
Moore talked to Parker's son, David. Then, without giving their father a chance to brush them off, 11 of his 12 children showed up at the store one day last year and drove him to a hospital.