Apple has a post about reccomended wifi settings for your router, as they do not believe that it is their software being glitchy, but the interference between bands (I've had the issue as well. See https://support.apple.com/en-ca/HT202068 or see below)

2.4 GHz channel width

Channel width controls how large of a ”pipe” is available to transfer data. However, larger channels are more subject to interference and more likely to interfere with other devices. A 40 MHz channel is sometimes called a wide channel, and a 20 MHz channel is a narrow channel.

Set to: 20 MHz

Use 20 MHz channels in the 2.4 GHz band. Using 40 MHz channels in the 2.4 GHz band can cause performance and reliability issues with your network, especially in the presence of other Wi-Fi networks and other 2.4 GHz devices. A 40 MHz channel might also cause interference and issues with other devices that use this band, such as Bluetooth devices, cordless phones, and neighboring Wi-Fi networks. Routers that don't support 40 MHz channels in the 2.4 GHz band do support 20 MHz channels.

5 GHz channel width

Channel width controls how large of a "pipe" is available to transfer data. Larger channels are more susceptible to interference, and more likely to interfere with other devices. Interference is less of an issue in the 5 GHz band than in the 2.4 GHz band. A 40 MHz channel is sometimes called a wide channel, and a 20 MHz channel is a narrow channel.

Set to: For 802.11n access points, set the 5GHz band to 20 MHz and 40 MHz. For 802.11ac access points, set the 5GHz band to 20 MHz, 40 MHz, and 80 MHz.

For best performance and reliability, enable support for all channel widths. This allows devices to use the largest width they support, which results in optimal performance and compatibility. Not all client devices support 40 MHz channels, so don't enable 40 MHz-only mode. Devices that support only 20 MHz channels cant connect to a Wi-Fi router in 40 MHz-only mode. Similarly, don't enable 80 MHz-only mode, or only clients capable of 802.11ac will be able to connect. Routers that don't support 40 MHz or 80 MHz channels do support 20 MHz channels.

WMM

WMM (Wi-Fi Multimedia) prioritizes network traffic according to four access categories: voice, video, best effort, and background.

Set to: Enabled

All 802.11n and 802.11ac access points should have WMM enabled in their default configuration. Disabling WMM can cause issues for the entire network, not just Apple products on the network.

MAC address authentication or filtering

Restricts access to a Wi-Fi router to devices with specific MAC (Media Access Control) addresses.

Set to: Disabled

When enabled, this feature allows a user to configure a list of MAC addresses for the Wi-Fi router, and restrict access to devices with addresses that are on the list. Devices with MAC addresses not on the list will fail to associate with the Wi-Fi network. MAC addresses can be changed easily, so don't rely on them to prevent unauthorized access to the network. iOS 8 and later uses a randomized MAC address when running Wi-Fi scans. The scans are conducted when a device isn't associated with a Wi-Fi network and its processor is asleep. A device’s processor goes to sleep shortly after the screen is turned off. Wi-Fi scans are run to determine if a user can connect to a preferred Wi-Fi network. Enhanced Wi-Fi scans are run when a device uses Location Services for apps that use geofencing, such as location-based reminders, that determine if the device is near a specific location.

My thinking is that the cable connecting to the airport card was damaged when I dropped the laptop. Does this seem likely?

You need to diagnose the issue and without actually putting "hands on" the unit itself, everything's just a guess at this point. That said, there's nothing in NVRAM or in power management (SMC) that resetting both/either will solve.

The "No WiFi hardware installed" means the hardware isn't being detected by macOS.

There are three possibilities:

• It's has a loose connection.
• The airport card is failing (possibly coincidental with your drop).
• The connector is broken

The first one is easy to diagnose/solve; simply disconnect, ensure that connections are clean, and then reconnect.

If the airport card has failed, you need to replace it with new Airport Adapter.

Finally, if the connectors are broken, you can either replace the cable as you initially thought or if it's on the logic board side, you will need to have the logic board repaired/replaced.