Inventing convenient excuses for why the tech doesn't work this time is a time-honoured Star Trek tradition
This question has been answered already, but I'd like to add that there are numerous instances in the various Star Trek series where the writers encountered this very issue. Here are some of the ways they solved it:
1. Using the transporter to save the day
The transporter frequently doesn't work. We're out of transporter range. We can't transport without lowering our shields / them lowering their shields. We can't get a transporter lock. We can't beam through the planet's unusually strong ionosphere. Ambassador Odan's people refuse to use transporters. The plasma fire is interfering with the transporters. And, quite commonly, there's too much interference, Captain!
And when they can use the transporter, there's often some limitation that makes the adventure non-trivial. We can't beam directly to the site without being spotted by the enemy / due to interference from the thing at the target site / due to high concentrations of magnesite ore in the surrounding hills / due to the target being too far underground, so we have to set down fifty kilometers away in the jungle.
Star Trek is also inconsistent as to what magic the transporters can do. They can restore Janeway and Paris after they were turned into amphibians in Threshold, but can't restore Neelix's lungs in Phage.
2. Allowing the tricorder or sensors to give away everything
Sensors suffer the same limitations that transporters do. Sensors cannot penetrate the planet's ionosphere. The Jem'Hadar ship came from the opposite side of the anomaly, so we couldn't detect it. The Romulans must be using a new kind of cloak, one we can't detect. We can't scan through this much solid rock; we'll have to send an away team.
Dax has to configure the tricorders to break the enemy encryption, so she can't use them as tricorders in the jungle. Sometimes the tricorders just give inconsistent readings or don't work. We need to get closer to the anomaly to scan it. The enemies took / disabled our weapons and transporters when we landed. There's too much interference.
Often, the sensors have arbitrary limits. They can find the missing away team / runabout, but it will take 8 hours to scan the entire planet's surface / sector where the ship was last seen.
3. Asking the computer for the answer to the issue at hand
COMPUTER: Searching. Darmok is the name of a seventh dynasty emperor on Kanda Four. A mytho-historical hunter on Shantil Three. A colony on Malindi Seven. A frozen dessert on Tazna Five. A....
TROI: Stop search. Computer, how many entries are there for Darmok?
COMPUTER: Forty seven.
The computer usually gives clues, but it never solves the puzzle right away. Star Trek's computer isn't intelligent or creative, it can only tell you exactly what you ask for. That's assuming you're on a fully equipped Galaxy-class starship, and not a runabout, on an away team, or a Cardassian station.
As the GM, you have to have adventures which cannot be solved by looking it up in the ship's computer. Starfleet sends ships to seek out new life and new civilizations, not look up information that's already known.
4. The Chief Engineer/Scientist/Doctor suddenly thinks up (i.e. rolls up) a brilliant solution from thin air.
That one tweet jokes how often they'd do this in TNG:
The Enterprise is flung into the Delta Quadrant by an alien called the Caretaker. Geordi soups up the warp core and they're home by dinner.
As often as this happens, however, there's an excuse for why that won't work. There'll be some complication or reason why it's not so simple. How about we do X? We can't, because Y. Unless we first did / found / destroyed / obtained Z, but that would require an entire action-packed adventure...
Often, the complications involved with actually implementing the doohicky form the focus of the episode, or it's in the background while the real conflict is about how they'll survive for six hours until the engineering department can get the doohicky online / the ship's sensors can locate the away team / Starfleet can send a rescue ship.
5. The non-human crew member suddenly finds a previously unknown special ability (Spock was the worst offender in this) that renders the plot point meaningless
Spock does this all the time, but it's considerably less common from TNG onward. Usually, it's about clever use of existing defined abilities, which is an excellent mode of play for an RPG (watch Jojo's Bizarre Adventure for a show which revolves around conflicts defined by creative use of existing abilities.)
Simply define that you cannot simply invent new character powers, and your players will generally understand this. It's a commonplace rule in RPGs.
6. Time travel in any form
Time travel is usually impossible without some doohickey which is generally both unavailable to the crew and expressly forbidden by Starfleet. When they get one, they usually lose it or give it up by the next episode.
There's always an excuse for why the solution that worked in the last episode won't work this time, or at least it won't solve the problem readily enough to to bypass the entire scenario instantly.