WASHINGTON — After weeks of simmering frustration, House Democrats took their first shot on Wednesday at questioning a key figure from Robert S. Mueller III’s investigation into whether President Trump obstructed justice. They were not entirely happy with the results.

Behind closed doors, lawmakers on the House Judiciary Committee pressed Hope Hicks, one of Mr. Trump’s closest former aides, for nearly seven hours on her recollections of contacts between the Trump campaign and Russia, as well as on episodes documented by Mr. Mueller, the special counsel, in which Mr. Trump tried to assert control over investigations into those contacts. And they resurrected an older accusation against Mr. Trump: his role in an illegal scheme to make hush payments to two women during his 2016 campaign.

But if the hearing held out the promise of kick-starting Democrats’ stalled investigations into Mr. Trump, it quickly veered toward an increasingly familiar outcome. It took place in private rather than public. And under the direction of the White House, Ms. Hicks declined to answer nearly every question about her time working in the administration, citing instructions from the president that she was “absolutely immune” from answering, lawmakers from both parties said.

At one point she refused, Democrats said, to even identify the location of her West Wing office.

Ms. Hicks did engage in queries about her work on the campaign, which is not subject to executive privilege or claims of immunity, discussing what she knew about contacts between Trump associates and Russia. But there was no immediate evidence that those exchanges produced meaningful new revelations. The Judiciary Committee said it intended to release a full transcript of the interview within 48 hours.