My.comp.wont.upgrade.to.Home.Premium....

Please attach the CheckSUR.log file to your reponse - we'll take a look at it (C:\Windows\Logs\CBS\CheckSUR.log)

What files are present in that folder?

run the following commands in an Elevated COmmand Prompt window

DIR C:\Windows\logs\CBS\*.*
ICACLS C:\Windows\logs\CBS

and copy/paste the results to your response.
Here are some instructions to make life easier :)
1) To open an Elevated Command Prompt Window (the CP window), click on Start, All Programs, Accessories – then right-click on Command Prompt, and select Run as Administrator. Accept the UAC prompt.
2) To run the commands easier, highlight the block of commands, and right-click on the highlight – select Copy. In the CP Windows, click on the black/white icon at top left – select Paste. The commands will run but may not complete the last command, so hit the Enter Key once.
3) To copy the results... click on the Black/White icon in the top left, and select Edit... 'Select All', and hit the Enter key - then use Ctrl+V or r-click+Paste to paste it into your response.

Okay, ready? here:

Microsoft Windows [Version 6.1.7601]
Copyright (c) 2009 Microsoft Corporation. All rights reserved.

C:\Windows\system32>DIR C:\Windows\logs\CBS\*.*
Volume in drive C is OS
Volume Serial Number is 125F-2925

Directory of C:\Windows\logs\CBS

06/24/2012 08:31 PM <DIR> .
06/24/2012 08:31 PM <DIR> ..
06/24/2012 08:41 PM 9,837 CBS.log
05/26/2012 03:19 AM 583,306 CbsPersist_20120526153256.cab
05/29/2012 06:11 PM 761,131 CbsPersist_20120530052756.cab
06/03/2012 10:16 PM 1,978,670 CbsPersist_20120604213040.cab
06/24/2012 01:21 AM 928,245 CbsPersist_20120624142000.cab
06/24/2012 11:46 AM 688,133 CbsPersist_20120624162534.cab
6 File(s) 4,949,322 bytes
2 Dir(s) 190,930,407,424 bytes free

C:\Windows\system32>ICACLS C:\Windows\logs\CBS
C:\Windows\logs\CBS NT SERVICE\TrustedInstallerI)(F)
NT SERVICE\TrustedInstallerI)(CI)(IO)(F)
NT AUTHORITY\SYSTEMI)(F)
NT AUTHORITY\SYSTEMI)(OI)(CI)(IO)(F)
BUILTIN\AdministratorsI)(F)
BUILTIN\AdministratorsI)(OI)(CI)(IO)(F)
BUILTIN\UsersI)(RX)
BUILTIN\UsersI)(OI)(CI)(IO)(GR,GE)
CREATOR OWNERI)(OI)(CI)(IO)(F)

Successfully processed 1 files; Failed processing 0 files

C:\Windows\system32>

That looks normal enough - except for the lack of a CheckSUR.log file.
This would tend to indicate that you haven't run the download, or that there were problems which prevented either the generation of the log, or saving it.
Since the log is started early in the process it may be that something interrupted it.
Try running the kb947821 download again, and takes note of what it's doing at the time (it can take 30 minutes or so to run, so be patient)
Then check for the log file again - atach it if found, and include any notes you took.

There should be a 120MB download from that link!
Here's the direct link for your version of the download - Download: System Update Readiness Tool for Windows 7 (KB947821) [May 2012] - Microsoft Download Center - Download Details
download and save it to the desktop, then double-click on the saved file to run it.

Please download the tool and run it, then attach the checkSUR to your response
Once step at a time! :)