The Launcher loads fine, but when I click "Play" it seems to be downloading 1.8.4.jar according to the status bar, then crashes, leaving me with this message in the Game Output section:

Error: Could not find or load main class net.minecraft.client.main.Main
Java HotSpot(TM) Client VM warning: Using incremental CMS is deprecated and will likely be removed in a future release

The last bit of my Launcher Log says:
[18:05:56 INFO]: Launching game
[18:05:56 INFO]: Unpacking natives to C:\Users\Tom\AppData\Roaming\.minecraft\versions\1.8.4\1.8.4-natives-166400697573155
[18:05:57 WARN]: No assets index file C:\Users\Tom\AppData\Roaming\.minecraft\assets\virtual\1.8; can't reconstruct assets
[18:05:57 INFO]: Launching in C:\Users\Tom\AppData\Roaming\.minecraft
[18:05:57 INFO]: Half command: C:\Program Files\Minecraft\runtime\jre-x32\1.8.0_25\bin\javaw.exe -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx512M -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M -Djava.library.path=C:\Users\Tom\AppData\Roaming\.minecraft\versions\1.8.4\1.8.4-natives-166400697573155 -cp C:\Users\Tom\AppData\Roaming\.minecraft\libraries\oshi-project\oshi-core\1.1\oshi-core-1.1.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\net\java\dev\jna\jna\3.4.0\jna-3.4.0.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\net\java\dev\jna\platform\3.4.0\platform-3.4.0.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\ibm\icu\icu4j-core-mojang\51.2\icu4j-core-mojang-51.2.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\net\sf\jopt-simple\jopt-simple\4.6\jopt-simple-4.6.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\paulscode\codecjorbis\20101023\codecjorbis-20101023.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\paulscode\codecwav\20101023\codecwav-20101023.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\paulscode\libraryjavasound\20101123\libraryjavasound-20101123.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\paulscode\librarylwjglopenal\20100824\librarylwjglopenal-20100824.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\paulscode\soundsystem\20120107\soundsystem-20120107.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\io\netty\netty-all\4.0.23.Final\netty-all-4.0.23.Final.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\google\guava\guava\17.0\guava-17.0.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\apache\commons\commons-lang3\3.3.2\commons-lang3-3.3.2.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\commons-io\commons-io\2.4\commons-io-2.4.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\commons-codec\commons-codec\1.9\commons-codec-1.9.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\net\java\jinput\jinput\2.0.5\jinput-2.0.5.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\net\java\jutils\jutils\1.0.0\jutils-1.0.0.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\google\code\gson\gson\2.2.4\gson-2.2.4.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\mojang\authlib\1.5.21\authlib-1.5.21.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\com\mojang\realms\1.7.14\realms-1.7.14.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\apache\commons\commons-compress\1.8.1\commons-compress-1.8.1.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\apache\httpcomponents\httpclient\4.3.3\httpclient-4.3.3.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\commons-logging\commons-logging\1.1.3\commons-logging-1.1.3.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\apache\httpcomponents\httpcore\4.3.2\httpcore-4.3.2.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\apache\logging\log4j\log4j-api\2.0-beta9\log4j-api-2.0-beta9.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\apache\logging\log4j\log4j-core\2.0-beta9\log4j-core-2.0-beta9.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\lwjgl\lwjgl\lwjgl\2.9.4-nightly-20150209\lwjgl-2.9.4-nightly-20150209.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\org\lwjgl\lwjgl\lwjgl_util\2.9.4-nightly-20150209\lwjgl_util-2.9.4-nightly-20150209.jar;C:\Users\Tom\AppData\Roaming\.minecraft\libraries\tv\twitch\twitch\6.5\twitch-6.5.jar;C:\Users\Tom\AppData\Roaming\.minecraft\versions\1.8.4\1.8.4.jar net.minecraft.client.main.Main
[18:05:57 INFO]: Looking for orphaned versions to clean up...
[18:05:57 INFO]: Looking for old natives & assets to clean up...
[18:05:57 ERROR]: Game ended with bad state (exit code 1)
[18:05:57 INFO]: Ignoring visibility rule and showing launcher due to a game crash
[18:05:57 INFO]: Deleting C:\Users\Tom\AppData\Roaming\.minecraft\versions\1.8.4\1.8.4-natives-166400697573155

Apologies for posting here if I've made an obvious error, but I have removed both Minecraft and Java, run registry cleaners and reinstalled from scratch several times without success, and spent 60 minutes searching for a solution without any success.

Can anyone help me?