Giants sign one-time 1,000-yard back Peyton Hillis

The Giants were hoping they could stabilize their running back situation until they get Andre Brown back in the second half of the season. Much like everything that has gone wrong for the winless Giants, they didn’t come close.

Mired near the bottom as the NFL’s 30th-ranked rushing team, the Giants could not wait for Brown’ return, as their running backs fell by the wayside. They added to a group on Wednesday that, to be kind, is eclectic by signing Peyton Hillis, who had one great season with the Browns.

“I’m coming in with an open heart and open mind,” Hillis said, “and I’m looking to do whatever the coaching staff needs me to do to help this team win.”

The 245-pound Hillis joins 265-pound Brandon Jacobs, who like Hillis was out of football waiting for a call when the Giants reached out. Jacobs was summoned after the first game of the season. The two bruisers are also similar in that their best days are behind them, although Jacobs dusted himself off last week in a vintage 22-carry, 106-yard, two-touchdown performance in a loss to the Bears in Chicago.

Hillis, 27, was signed from Tuesday’s five-player tryout. If this signing had taken place three years ago, it would have been a big deal. He rose to prominence in 2010 with the Browns, rushing for 1,177 yards and 11 touchdowns and became so popular he won a national voting contest to be on the cover of Madden NFL 12.

Hillis hasn’t risen as high since then. Originally a 2008 seventh-round pick of the Broncos out of Arkansas, Hillis could not follow up his breakout season. Slowed by a torn hamstring and beset with contract issues, he gained 587 yard for the Browns in 2011 and 309 yards for the Chiefs in 2012. He was briefly with the Buccaneers this season before being released. Hillis has started 33 games in his six-year NFL career.

“I firmly believe I never had too much of an opportunity after I left Cleveland,” Hillis said. “I was behind Jamaal Charles at Kansas City. I didn’t get too much playing time. I felt when I got in I did well, and then I was in Tampa and never really got to touch the field because of Doug Martin.’’

Hillis was part of a running back tryout that included former Giants D.J. Ware and Ryan Torain, plus rookies Jeremy Wright and Donald Russell.

The need for a new running back arose because David Wilson remains out with a herniated disk in his neck and Da’Rel Scott was waived on Tuesday with a hamstring injury. The only other running backs on the roster were Jacobs and rookie Michael Cox. Jacobs has a slight hamstring strain, but said he should be fine for Monday night’s game against the Vikings. Cox has yet to get an NFL rushing attempt in his first season.

The clock has been restarted for Brown, who was placed on injured reserve/designated for return after he refractured his left leg Aug. 29 in the preseason finale against the Patriots at Gillette Stadium. Brown can resume practicing this week — he expects to work in individual drills on Thursday — and can be activated to play after the eighth game of the season, meaning he could be on the field Nov. 10 to face the Raiders.

“I want to play. It hurts not going out there and playing with the guys,’’ Brown told The Post. “I definitely want to go back out there and try to help them get this thing turned around. It’s eating me up inside. I just want to go out there and compete and hit somebody.’’

Brown, a 2009 fourth-round pick of the Giants, received his first significant chance to play in 2012 after bouncing from team to team. He gained 385 yards and averaged 5.3 yards per carry before fracturing his left fibula Nov. 25 in a victory over the Packers. He was fully healthy heading into this season and expected to be part of the 1-2 punch with Wilson, providing the muscle to augment Wilson’s speed.

Hillis hopes he can quickly learn the Giants system. Coming from the Bucs, he should already have a head start, as Bucs offensive coordinator Mike Sullivan was the Giants receivers coach and took that offense with him to Tampa.

“From what I understand, a lot of the terminology is the same as it was in Tampa, and so it may be a quick process,” Hillis said. “Maybe, maybe not. We’ll see.’’