Can I travel inside the US with a digital copy of my passport and visa?

You don't need your passport. If you're within 100 miles of the Mexican or Canadian border, you may be stopped by US Border Patrol. They will typically ask you if you are a US citizen, and, when you answer "no," they will want evidence of your immigration status.

The US statute that they'll cite, if they cite anything at all, will be 8 USC 1304, Forms for registration and fingerprinting, which says at paragraph (e) that

Every alien, eighteen years of age and over, shall at all times carry with him and have in his personal possession any certificate of alien registration or alien registration receipt card issued to him pursuant to subsection (d). Any alien who fails to comply with the provisions of this subsection shall be guilty of a misdemeanor and shall upon conviction for each offense be fined not to exceed $100 or be imprisoned not more than thirty days, or both.

For reference, here is subsection (d):

Every alien in the United States who has been registered and fingerprinted under the provisions of the Alien Registration Act, 1940, or under the provisions of this chapter shall be issued a certificate of alien registration or an alien registration receipt card in such form and manner and at such time as shall be prescribed under regulations issued by the Attorney General.

Now it's not clear to me whether the fingerprinting that visitors undergo when they enter the US is "under the provisions of the Alien Registration Act, 1940, or under the provisions of this chapter," but for the sake of discussion, let us assume that it is.

At 8 CFR 264.1, you can learn that your I-94 form is both a "prescribed registration form" and "evidence of registration." Your passport with its admission stamp is also "evidence of registration."

In the exceedingly unlikely event that you were cited for violating 8 USC 1304 (e), you would probably be able to defend yourself successfully by showing that you had your I-94A with you. But the only prosecutions I've found under this section were people who were being prosecuted for much more serious criminal violations, and this one was just added to the list.

If you don't have either of these documents, they'll look you up in the database, determine that you're in the country legally, and let you go. They might take you to the office to do this, so it's something you'd rather avoid. Having a digital copy of your passport might help with this, and having your I-94A certainly will.

I presume you sent your passport to the consulate for a visa. If you have a reasonable explanation for why you don't have your passport, you're unlikely to be given trouble for not having it.

Finally, these rules apply at all times. It doesn't matter whether you're going to another state or just popping around the corner for a hot dog, or even just sitting in your hotel room. If the law were taken completely literally, as Border Patrol officers seem to insist, it would be illegal for foreigners to mail their passports to consulates altogether.