MacOS – Mountain Lion, System Preferences and App Store crash, Clean Install doesn’t help

Background – Mid-2010 MBP 13", upgraded to 8 GB memory. Came with Snow Leopard, Upgraded to Lion without clean install. Worked perfectly. Have CleanMyMac installed on it.

Problem – After upgrade to Mountain Lion, again, update from App Store, no clean install, the App Store and the System Preferences would crash. The app store just opens and hits the beach ball and SYstem prefs hits beach call on opening "Security" or on trying to add a twitter account to the Mail settings.

Analysis – Some forum said that CleanMyMac deletes the Intel based execs some times when cleaning up, which causes this problem. Did not encounter this during my entire use of Lion, so not sure if true.

I started both System prefs and App store with Sudo. They worked. But again, System prefs crashed on opening the Security settings with the note that this cannot be opened on a non-Intel Mac. (LoL)

What I've done – I backed up everything on Time Machine and did a clean install. How? I went into the recovery partition and wiped my main HDD and then Asked it to install ML. It downloaded a fresh copy of ML and installed it. Then, I thought, hey all done and I asked it to restore from Time Machine when the prompt came up. (I think this was a mistake). Again, after this whole process, App store and System prefs crash.

Point to be noted – when I open "Software Update", the app store opens perfectly. But when I try to navigate towards the normal app store sections from there, it crashes.

What I need from all you amazing readers –
1. What is your analysis? How can this issue be resolved?

1. Is there a way that I can restore all my personal info and my apps from my Time Machine backup but not the App Store or the System Prefs apps, so that they have a pure, clean install?

2. If anyone needs to see a crash log, I have one sitting in a droplr note, so if you need to see how my System Prefs app crashed, just ask in the comments.

Apologies – If this seems to be a very common problem and my question is repetitive, but StackExchange's filters showed me nothing specific to ML, so I asked.

Thanks!!!

From the Console –

7/31/12 6:23:47.234 PM accountsd[20958]: Error while opening database Error Domain=NSCocoaErrorDomain Code=512 "The file couldn’t be saved." UserInfo=0x7fa603426ae0 {reason=Failed to create file; code = 2}, {
reason = "Failed to create file; code = 2";
}

Creating new database...
7/31/12 6:23:47.236 PM accountsd[20958]: Second Error while creating new database Error Domain=NSCocoaErrorDomain Code=512 "The file couldn’t be saved." UserInfo=0x7fa6034355d0 {reason=Failed to create file; code = 2}, {
reason = "Failed to create file; code = 2";
}
7/31/12 6:23:47.809 PM com.apple.launchd.peruser.501[1189]: (com.apple.accountsd[20958]) Job appears to have crashed: Abort trap: 6
7/31/12 6:23:47.809 PM com.apple.launchd.peruser.501[1189]: (com.apple.accountsd) Throttling respawn: Will start in 10 seconds
7/31/12 6:23:47.899 PM ReportCrash[20904]: File creation failed /Users/nitinthewiz/Library/Logs/DiagnosticReports/accountsd_2012-07-31-182347_nitin.crash - uid: 501 gid: 20, euid: 501 egid: 20 - error 2: No such file or directory
7/31/12 6:23:47.900 PM ReportCrash[20904]: Failed to save crash report for accountsd[20958] (version 182.2 (182.2)) to file://localhost/Users/nitinthewiz/Library/Logs/DiagnosticReports/accountsd_2012-07-31-182347_nitin.crash.
7/31/12 6:23:47.905 PM ReportCrash[20904]: Process:         accountsd [20958]
7/31/12 6:23:47.905 PM ReportCrash[20904]: Path:            /System/Library/Frameworks/Accounts.framework/Versions/A/Support/accountsd
7/31/12 6:23:47.905 PM ReportCrash[20904]: Identifier:      accountsd
7/31/12 6:23:47.905 PM ReportCrash[20904]: Version:         182.2 (182.2)
7/31/12 6:23:47.905 PM ReportCrash[20904]: Code Type:       X86-64 (Native)
7/31/12 6:23:47.905 PM ReportCrash[20904]: Parent Process:  launchd [1189]
7/31/12 6:23:47.905 PM ReportCrash[20904]: User ID:         501
7/31/12 6:23:47.906 PM ReportCrash[20904]:  
7/31/12 6:23:47.906 PM ReportCrash[20904]: Date/Time:       2012-07-31 18:23:47.235 -0600

Update –

Ok, I've got some updates to give. I did a clean install. This time, I did not recover stuff from my Time Machine. It all worked. So, now the question transforms to selective Time Machine backup.

Remember, my apps are all working now, But I am sure that the settings/App files in my Time Machine are corrupted. So, I do want to recover all my personal files and all the 3rd Party apps that I once had, but I do not want the following –

1. The System Prefs app files and the App Store App files must not be restored
2. Any settings related to the above apps must not be restored.

Can Time Machine do such selective restoring?
If I restore my entire home folder, will I also be restoring the faulty settings related to the crashing apps?
Can I recover selective apps from Time Machine?

These are the questions plaguing my evening. Anyone who can help is more than welcome!