The Dell Reinstallation DVD should be fine, if it is media made by Dell DataSafe then a Reinstallation DVD should be used or requested. All the Reinstallation DVD has is SLP activation and a couple of OEM logos otherwise it is identical to the retail media.
Ensure that all Microsoft Software with the latest Service Pack is installed before the system drivers. e.g. install Windows 7 with Service Pack 1, Office 2010 with Service Pack 1, Visio 2010 with Service Pack 1, Internet Explorer 9, Microsoft Mathematics etc. before the drivers.
Please follow my wiki A Clean Install of Windows 7/Windows Reinstallation Guide: http://en.community.dell.com/support-forums/software-os/f/3524/t/19480753.aspx Ensure that Service Pack 1 (if not included on the DVD is installed before the system drivers).
Ensure that Office 2010 with Service Pack 1 is installed (before the drivers). Get an Office 2010 with Service Pack 1 installer from here: http://www.heidoc.net/joomla/technology-science/microsoft/18-office-2010-direct-download-links
Also when installing your Video Card Driver (I'm not sure what one you have) but get the driver direct from ATI or nVidea opposed to using the one on the Dell drivers and downloads page. Its possible that it is a video card update from Windows Update is causing the problem. A clean install using directly the latest driver could help. I would also recommend a full wipe of the system using DBAN before beginning the Windows installation as mentioned in Step 7a of A Clean Install of Windows 7. There may be some hidden Malware that AVG can't find and DBAN will be rid of it (a scan with Malwarebytes' AntiMalware might also be a good idea). http://support.microsoft.com/kb/2694911
For the other system drivers I would use the later version from the XPS 8300:
R284334 Intel H67 Chipset (should aloso contain the files for the H57 Chipset)
R284362 Intel AMT HECI Chipset
R284354 Intel Rapid Storage Technology
R282233 Broadcom BCM57788 LOM
R282239 Realtek ALC887 HD Audio
R281588 Card Reader
R283190 Bluetooth 365 if you have it
Also temporarily ditch AVG and use Microsoft Security Essentials as AVG could be causing the problem. Edit: you said you got the problems without AVG. What other security do you have and are you running any registry cleaning/optimisation programs (these should be avoided)?
In addition reseat your memory modules and graphics card. I had some freezing problems in the past when my graphics card was only so slightly loose. However if this only happens after updates I would assume that it is a software issue and not this.
