Installation freeze on Setup is Starting... screen

This started with first being unable to boot Windows at all. Booting led windows to start with no interface. I could move the mouse pointer on a blank screen and that was it. Same thing happened while attempting to use my set of recovery disks.
Finally I downloaded an .iso and attempted a fresh install, with the result that it froze before setup even started (just after the language settings screen).

(Windows came pre-installed - but I removed the hidden partition on which the setup was kept some time ago, after making the recovery disks)
I've spent several days searching the Internet for possible solutions, but none of them have worked: Limiting RAM, using a different dvd... Nothing changes.

Using Linux I've determined that the hard drive has no bad clusters, and that the computer can indeed still install and run an operating system without issues.

Any ideas?

Try cleaning your DVD Drive.

I did that between the two DVDs I burned.

Where do you buy your DVD from?

Back up your files, unplug all other HD's and peripherals,

Boot into BIOS setup to enable Legacy BIOS if present. Next check BIOS Boot order for an EFI Boot Disk and if present remove it, set DVD drive first to boot, HD second. Then set SATA controller to AHCI. Save changes and Exit.

Then boot into installer DVD or flash stick burned or written using tool and latest ISO for your licensed OS version here.

At first installer screen Press Shift + F10 to open a Command Box, type:

DISKPART
LIST DISK
SELECT DISK 0 (after confirming Windows 7 target HD #)
CLEAN
CREATE PARTITION PRIMARY SIZE=102400 (for 100gb partition, adjust as desired)
FORMAT FS=NTFS LABEL="WINDOWS 7"
ACTIVE
EXIT
EXIT

Next click Install Now to Clean Install Windows 7 to the partition you created. If it fails then report back at which step and the verbatim error message.

In addition read over these steps to understand the tools and methods which work best to get and maintain a perfect Clean Reinstall - Factory OEM Windows 7. The steps are the same for retail.

Dumb BIOS. No Legacy support, no options for SATA controller. DVD is already set to boot first.
DISKPART fails to provide a prompt. Freezes after displaying version, copyright and "on computer: MINWINPC". No error message. Just doesn't work.

This is extremely frustrating. All Windows/microsoft things freeze before they get anywhere, yet scans indicate nothing at all wrong with my computer.

I really have no idea what could possibly be preventing these things from starting.

Test your RAM - Test with Memtest86+ for 5-6 passes or overnight.

Test the HDD with maker's HD Diagnostic extended CD scan.

Reset the BIOS to defaults: Clear CMOS - 3 Ways to Clear the CMOS - Reset BIOS
Set DVD drive again to boot first, or trigger it using F8 key at boot.

Now try booting the Win7 DVD to install, deleting all partitions as shown in Steps 6-7 in Clean Install Windows 7.

Well, gregrocker, this resulted in no change to my situation. Drive is fine, RAM is fine, Windows setup still refuses to start.

Since you're able to boot a Linux disk, can you wipe the HD? If not use the HD Diagnostics CD which autostarts to do a Quick Wipe.

This should force the installer to boot and give it a cleaner slate to overcome any blockage.

If it still won't load then try a new ISO burned both to DVD and Flash stick as provided in Steps 1,2 of Clean Reinstall - Factory OEM Windows 7. If DVD fails again, disconnect it's drive and try booting flash stick using one-time BIOS Boot Menu key under USB, Removable or HD's. You may need to expand a listing to choose it.