Seeking a builder to cooperate on the project, Mr. Grimm chose a former F.B.I. agent who had served with him in New York — even though the former agent was under indictment on state racketeering and fraud charges, according to court and property records. The former agent, Carlos Luquis, was soon convicted for his role in skimming $2 million from Texans’ electric bills, and served 18 months in prison. Yet Mr. Grimm went on to do business with Mr. Luquis and his wife in two other companies, records show. And during Mr. Grimm’s successful insurgent campaign for Congress in 2010, Mr. Luquis was frequently at his side. Mr. Grimm’s ties to Mr. Luquis reflect a checkered business background that seems to clash in some ways with his image as a straight-arrow veteran of the Marine Corps and the F.B.I. That image has been crucial to his ascent in the Republican Party. Before becoming an F.B.I. agent for a decade, Mr. Grimm worked for a year for a small firm on Wall Street that frequently ran into problems with regulators and customers, regulatory filings show. But his official biographies do not mention the firm, Whale Securities. After he left the bureau, he opened a restaurant in Manhattan that has been accused in a lawsuit of cheating its workers and fined by the state for failing to carry workers’ compensation. Mr. Grimm, who represents Staten Island and part of Brooklyn, is facing scrutiny after The New York Times reported last month that the F.B.I. was investigating his main fund-raiser in the 2010 race. The fund-raiser, Ofer Biton, helped Mr. Grimm collect more than $500,000 in campaign donations from the followers of an Israeli rabbi and mystic, a vast majority of whom do not live in the Congressional district. Followers of the rabbi have told The Times that Mr. Grimm or Mr. Biton informed them the campaign would find ways to accept illegal donations, including those that exceeded limits, were paid in cash or came from foreigners without green cards. The F.B.I. is examining allegations that Mr. Biton embezzled millions of dollars from the rabbi’s congregation. Mr. Grimm has said he never violated the law, but declined to answer questions about his fund-raising. The Times sent Mr. Grimm questions last week about his business activities and associates. Mr. Grimm responded with an official statement. “Like many small-business owners, I have experienced successes as well as setbacks,” he said. “But I have tried to face adversity the same way that I have met every challenge in my life: ethically and lawfully.” He added: “I have relied as a businessman on the same principles of honesty that have guided my service as a Marine, an F.B.I. special agent and as a United States congressman. This attack is politically motivated, as my record as an effective congressman, fighting for Staten Island and Brooklyn, cannot be denied.” Friends and political allies described Mr. Grimm as honest and patriotic. Jack Garcia, a retired F.B.I. agent who is well regarded for putting organized-crime figures behind bars, said he worked with Mr. Grimm on undercover operations. Mr. Garcia said Mr. Grimm was a master of playing the roles of criminals — money launderer, corrupt stock broker — and would “never in a million years” commit an impropriety. Mr. Grimm’s political ascent has been based on that reputation. But along the way, Mr. Grimm met friction from some fellow Republicans on Staten Island. In 2010, the borough’s party committee took an unusual step: endorsing a Brooklynite for the House seat. (Mr. Grimm nonetheless won the primary and defeated the Democratic incumbent.) Two people familiar with the committee’s deliberations said in interviews that it did not endorse Mr. Grimm partly because he gave vague answers when asked why he left the F.B.I. after a decade — and what he did afterward. Public records reveal some answers. Mr. Grimm and Mr. Luquis, the former F.B.I. agent convicted in Texas, were colleagues in the bureau for five years, from 1998 to 2003. Mr. Luquis then left for a job at the Electric Reliability Council of Texas, a publicly subsidized nonprofit group that helps to manage the electrical grid. In 2005, Mr. Luquis and five accomplices were charged with stealing $2 million from electricity customers. In May 2006, days after Mr. Grimm left the F.B.I., he and a partner, Harold Rosenbaum, borrowed $1.34 million from a bank and agreed to pay $965,000 to Mr. Luquis’s company, Hill Castle Homes, to build a house near Austin, Tex., according to property and court records. The records show that they agreed to work with Mr. Luquis’s company even earlier, in March 2006, when Mr. Grimm was an F.B.I. agent. By May 25, 2006, when Mr. Luquis signed a contract on the deal, he was weeks away from trial, at which he was convicted and sentenced to 12 years in prison. F.B.I. officials flew in and testified during the sentencing phase that Mr. Luquis had also exaggerated his role in investigating the Sept. 11 attacks. Three years later, the land deal had soured, and Mr. Grimm sought to be released from a debt to a craftsman who worked on the house.