They were working just earlier today. I rebooted a few times for unrelated reasons. Opened up the same document and noticed spelling and grammar checks no longer work. I tried the work around Fatal error - #3 by manj_k - but it didn’t work.
I tried renaming the “extensions” folder in %appdata%\LibreOffice\3\user\extensions, and also C:\Program Files (x86)\LibreOffice 3.6\share
Nothing 
The above-mentioned workaround isn’t necessary for LibreOffice 3.6.1. (The bug has been fixed in this version).
And renaming the folder "extensions" in C:\Program Files (x86)\LibreOffice 3.6\share is in any case the wrong approach.
If related to a “bundled” dictionary:
(1) Close LibreOffice (+ Quickstarter, if enabled),
right click on LibO_3.6.1.2_Win_x86_install_multi.msi → Repair
(Then test Spellcheck/AutoSpellcheck)
(2) Check Menu `Tools → Options → Language Settings → Writing Aids → Available language modules → Edit… (ABC checkmarks?)
(3) Set the cursor in a misspelled word.
What language is shown in the Status Bar?
Check the language via Menu Format → Character... → Font → Language.
If related to a “per-user” installed dictionary extension:
(1) Uninstall and reinstall the extension via Extension Manager.
(2), (3) see above…