Quick Answer
Losing all satellites would disrupt many systems but would not make the internet disappear everywhere. Terrestrial fiber, cables, towers and data centers would continue where powered. GPS and other satellite navigation systems would be lost, weather observations would degrade, some communications and broadcasting would be disrupted, and many scientific missions would end immediately.
Modern society uses satellites for far more than television. Orbiting spacecraft provide positioning, timing, weather observations, Earth imaging, scientific measurements and some communication links. Removing all of them would create a large technological blind spot.
GPS would vanish
GPS is one of several global navigation satellite systems. If every satellite disappeared, receivers would no longer obtain the normal satellite timing and ranging signals. Navigation could fall back on inertial systems, maps, radio beacons and other terrestrial methods, but the convenience and global coverage of satellite positioning would be gone.
Weather forecasting gets harder
Weather satellites observe clouds, storms, atmospheric moisture, ocean conditions and other variables over huge areas. Ground stations and aircraft would still provide observations, but losing orbital coverage would reduce the amount and geographic reach of data available to forecasters.
The internet would not disappear
Most everyday internet traffic travels through terrestrial and submarine fiber-optic networks, not satellites. Some remote regions and specialized services rely more heavily on satellite connectivity, so their disruption would be much larger. But deleting satellites is not equivalent to unplugging the global internet.
Timing matters too
Navigation satellites provide highly accurate timing signals used by some communications, financial and infrastructure systems. Losing those signals would force affected systems to rely on terrestrial clocks and alternative synchronization methods.
Established scienceSatellite navigation systems provide positioning, navigation and precise timing. They are important infrastructure, but they are not the only source of timing or communication, so the consequences would differ between sectors.
Scientific research
Earth-observing missions, space telescopes and scientific spacecraft would be lost. Researchers would lose continuous measurements that cannot be reproduced from the ground, including observations of the atmosphere, oceans, land surface and distant astronomical objects.
The bottom line
A satellite-free world would still have electricity, fiber networks, radio towers and computers. But it would lose a global layer of positioning, timing, observation and communication that modern systems increasingly assume exists.