A couple things you could do to help try and sove the problem.
1) If you are Overclocking set you speed to 600max.
2) Open command prompt and run the following command
It won't print out anything but let it run in the background then go try and download a app wait till it either freezes or reboots then count to 30 do ctrl+c which will stop the log then attach the logcat.txt to your post.
I am not overclocking.
This appears to be the important part. The rest just seemed like startup information.
--------- beginning of /dev/log/system
I/Vold ( 1193): Vold 2.1 (the revenge) firing up
D/Vold ( 1193): Volume sdcard state changing -1 (Initializing) -> 0 (No-Media)
D/Vold ( 1193): Volume sdcard state changing 0 (No-Media) -> 2 (Pending)
D/Vold ( 1193): Volume sdcard state changing 2 (Pending) -> 1 (Idle-Unmounted)
I/SystemServer( 1509): Entered the Android system server!
I/SystemServer( 1509): Entropy Service
I/SystemServer( 1509): Power Manager
I/SystemServer( 1509): Activity Manager
I/ActivityManager( 1509): Memory class: 32
I/SystemServer( 1509): Telephony Registry
I/SystemServer( 1509): Package Manager
I/Installer( 1509): connecting...
E/PackageManager( 1509): Package com.lge.internal has no signatures that match those in shared user android.uid.system; ignoring!
I/PackageManager( 1509): Time to scan packages: 4.44 seconds
W/PackageManager( 1509): Unknown permission android.permission.ADD_SYSTEM_SERVICE in package com.android.phone
W/PackageManager( 1509): Unknown permission android.permission.READ_SETTINGS in package com.lge.hiddenmenu
W/PackageManager( 1509): Unknown permission android.permission.READ_ERS in package com.lge.hiddenmenu
W/PackageManager( 1509): Unknown permission android.permission.WRITE_ERS in package com.lge.hiddenmenu
W/PackageManager( 1509): Unknown permission android.permission.ACCESS_LGDRM in package com.lge.hiddenmenu
W/PackageManager( 1509): Unknown permission com.google.android.apps.googlevoice.permission.AUTO_SEND in package com.google.android.voicesearch
W/PackageManager( 1509): Unknown permission com.android.launcher.permission.INSTALL_SHORTCUT in package com.android.browser
W/PackageManager( 1509): Unknown permission com.google.android.providers.gmail.permission.READ_GMAIL in package com.android.music
W/PackageManager( 1509): Unknown permission com.google.android.providers.gmail.permission.READ_GMAIL in package com.fede.launcher
W/PackageManager( 1509): Unknown permission com.android.launcher.permission.READ_SETTINGS in package com.android.settings
W/PackageManager( 1509): Unknown permission com.android.launcher.permission.WRITE_SETTINGS in package com.android.settings
W/PackageManager( 1509): Not granting permission android.permission.SEND_DOWNLOAD_COMPLETED_INTENTS to package com.android.vending (protectionLevel=2 flags=0x2be05)
W/PackageManager( 1509): Unknown permission android.permission.SEND in package com.android.vending
W/PackageManager( 1509): Unknown permission com.android.providers.im.permission.READ_ONLY in package com.google.android.apps.maps
W/PackageManager( 1509): Unknown permission com.android.launcher.permission.INSTALL_SHORTCUT in package com.google.android.apps.maps
W/PackageManager( 1509): Unknown permission android.permission.ACCESS_GPS in package com.telenav.app.android.sprint
W/PackageManager( 1509): Unknown permission android.permission.ACCESS_LOCATION in package com.telenav.app.android.sprint
W/PackageManager( 1509): Unknown permission android.permission.READ_EXTERNAL_STORAGE in package com.lge.LgHiddenMenu
I/SystemServer( 1509): Account Manager