I have no issue selecting a word in an email body and searching for it. in the search dialog using copy and paste. Perhaps you have an incompatible addon.

I see no problems

My only addons are filelink for dropbox and provider for google calendar. I can neither cut nor paste in my search box. I'm using Windows 10, everything is up to date.

To diagnose problems with Thunderbird, try the following:

• Restart Thunderbird with add-ons disabled (Thunderbird Safe Mode). On the Help menu, click on "Restart with Add-ons Disabled". If Thunderbird works like normal, there is an Add-on or Theme interfering with normal operations. You will need to re-enable add-ons one at a time until you locate the offender.
• Restart the operating system in safe mode with Networking. This loads only the very basics needed to start your computer while enabling an Internet connection. Click on your operating system for instructions on how to start in safe mode: Windows 10, Windows 8, Windows 7, Windows Vista, Windows XP, OSX

If safe mode for the operating system fixes the issue, there's other software in your computer that's causing problems. Possibilities include but not limited to: AV scanning, virus/malware, background downloads such as program updates.

My only extensions were Filelink Provider for Dropbox and Provider for Google Calendar. I disabled them and restarted Thunderbird, "search messages" was grayed out. I then re-enabled them, restarted Thunderbird, and now the search function appears to be working again. An email I'd been trying to locate earlier this evening with no results came back immediately this time.