[Eee Pad Transformer Q&A, Help & Troubleshooting] FairlightLion:
If it helps, here's the bit in the log that comes before the crash looping starts:

(Also, if it helps, CyanogenMod 10 works.. but that's still Android 4.1, so.. hmm..)

D/dalvikvm( 728): WAIT_FOR_CONCURRENT_GC blocked 6ms

D/dalvikvm( 728): WAIT_FOR_CONCURRENT_GC blocked 6ms

D/dalvikvm( 728): WAIT_FOR_CONCURRENT_GC blocked 7ms

E/ConnectivityService( 728): Ignoring protectedNetwork 10

E/ConnectivityService( 728): Ignoring protectedNetwork 11

E/ConnectivityService( 728): Ignoring protectedNetwork 12

D/BluetoothTethering( 728): startMonitoring: target: Handler (com.android.serve

r.ConnectivityService$NetworkStateTrackerHandler) {425cc2d8}

D/BluetoothManagerService( 728): Message: 20

D/BluetoothManagerService( 728): Added callback: android.bluetooth.BluetoothAda

pter$1@423890c0:true

D/BluetoothPan( 728): BluetoothPan() call bindService

D/BluetoothManagerService( 728): Message: 30

D/BluetoothPan( 728): BluetoothPan(), bindService called

W/ApplicationContext( 728): Calling a method in the system process without a qu

alified user: android.app.ContextImpl.bindService:1424 android.bluetooth.Bluetoo

thPan.<init>:141 android.bluetooth.BluetoothAdapter.getProfileProxy:1164

I/WifiService( 728): WifiService starting up with Wi-Fi disabled

D/WifiWatchdogStateMachine( 728): Disabling poor network avoidance for wi-fi on

ly device

I/SystemServer( 728): Network Service Discovery Service

D/NsdService( 728): Network service discovery enabled true

I/SystemServer( 728): Throttle Service

I/SystemServer( 728): UpdateLock Service

I/SystemServer( 728): Notification Manager

I/SystemServer( 728): Device Storage Monitor

I/SystemServer( 728): Location Manager

I/SystemServer( 728): Country Detector

I/SystemServer( 728): Search Service

I/SystemServer( 728): DropBox Service

I/SystemServer( 728): Wallpaper Service

W/WallpaperService( 728): failed parsing /data/system/users/0/wallpaper_info.xm

l java.io.FileNotFoundException: /data/system/users/0/wallpaper_info.xml: open f

ailed: ENOENT (No such file or directory)

I/SystemServer( 728): Audio Service

I/SystemServer( 728): Dock Observer

I/SystemServer( 728): Wired Accessory Manager

W/WiredAccessoryManager( 728): This kernel does not have usb audio support

I/SystemServer( 728): USB Service

I/SystemServer( 728): Serial Service

I/SystemServer( 728): Twilight Service

I/SystemServer( 728): UI Mode Manager Service

I/SystemServer( 728): Backup Service

V/BackupManagerService( 728): No ancestral data

D/dalvikvm( 728): GC_CONCURRENT freed 250K, 31% free 4711K/6744K, paused 4ms+3m

s, total 35ms

D/dalvikvm( 728): WAIT_FOR_CONCURRENT_GC blocked 5ms

D/dalvikvm( 728): WAIT_FOR_CONCURRENT_GC blocked 19ms

I/BackupManagerService( 728): Backup enabled => false

I/SystemServer( 728): AppWidget Service

I/SystemServer( 728): Recognition Service

I/SystemServer( 728): DiskStats Service

I/SystemServer( 728): SamplingProfiler Service

I/SystemServer( 728): NetworkTimeUpdateService

I/SystemServer( 728): CommonTimeManagementService

I/SystemServer( 728): CertBlacklister

I/SystemServer( 728): Dreams Service

I/WindowManager( 728): SAFE MODE not enabled

I/SystemServer( 728): AssetRedirectionManager Service

E/SQLiteLog( 728): (1) no such table: locksettings

I/LockSettingsService( 728): Migrated lock settings to new location

I/ActivityManager( 728): Sending system update to ComponentInfo{com.android.pro

viders.contacts/com.android.providers.contacts.ContactsUpgradeReceiver} for user

0

I/ActivityManager( 728): Sending system update to ComponentInfo{com.android.pro

viders.media/com.android.providers.media.MediaUpgradeReceiver} for user 0

I/ActivityManager( 728): Sending system update to ComponentInfo{com.android.pro

viders.calendar/com.android.providers.calendar.CalendarUpgradeReceiver} for user

0

I/ActivityManager( 728): Sending system update to ComponentInfo{com.google.andr

oid.gsf/com.google.android.gsf.loginservice.MigrateToAccountManagerBroadcastRece

iver} for user 0

I/SystemServer( 728): Enabled StrictMode for system server main thread.

I/Zygote ( 728): Process: zygote socket opened

E/dalvikvm( 926): cannot mountExternalStorage(): Success

E/dalvikvm( 926): VM aborting

F/libc ( 926): Fatal signal 11 (SIGSEGV) at 0xdeadd00d (code=1), thread 926

(zygote)

E/dalvikvm( 926): Storage environment undefined; unable to provide external sto

rage

I/ActivityManager( 728): Start proc android.process.acore for broadcast com.and

roid.providers.contacts/.ContactsUpgradeReceiver: pid=926 uid=10000 gids={50000,

3003, 1015, 1023, 1028}

I/DEBUG ( 97): *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *

**

I/DEBUG ( 97): Build fingerprint: 'asus/US_epad/TF101:4.0.3/IML74K/US_epad-9

.2.1.27-20120615:user/release-keys'

I/DEBUG ( 97): Revision: '0'

I/DEBUG ( 97): pid: 926, tid: 926, name: zygote >>> zygote <<<

I/DEBUG ( 97): signal 11 (SIGSEGV), code 1 (SEGV_MAPERR), fault addr deadd00

d

.. and so n, now looping the sig11 crash.