WLAN

virus/spyware/malware might have corrupted some Microsoft files.

http://www.microsoft.com/resources/documentation/windows/xp/all/proddocs/en-us/system_file_checker.mspx?mfr=true

sfc /scannow
this one should fix it if thats the case, you need your original DVD most of the times.

Also you could try to "uninstall" the WLAN from the device manager and reboot the laptop, after rebooting it, windows will try to reinstall it and could fix your problem.

I did the System File checker, CheckDisk & uninstall/reinstall adapter.

Windows repair ?
http://www.michaelstevenstech.com/XPrepairinstall.htm

Also check your BIOS, wireless could be disabled there too

I tried a repair install & it crashed. I restored it with an image & tried again. Now it won't copy all the files. I've tried 3 XP disks. I'm running another another CheckDisk, but no errors so far (stage 4).

Is the Wireless Zero Configurarion, and the the WWAN Autoconfig services started?

Hmm, a repair install crashes, what is that?!  Since when does a repair install result in crashing when the system prior to repair install doesn't?  Something doesn't make any sense with that eh.
I suspect you might be trying a repair install with a XP disc that doesn't include SP2 or SP3 or needed SATA motherboard drivers.  The original XP factory of said machine likely had post SP2 SATA drivers streamlined into it already.  Try making a XP CD with SP3 and SATA and mobo drivers streamlined into it.

Ditto "now it won't copy all the files", again, what is that?  Hmmm.  All three of your CDs are bad?  Seems a long shot, though not impossible, especially if tried to copy an already scratched one.  Still, seems possible CDROM drive is bad, or even your computers hard disk controller is malfunctioning, for both CDs and HD, which would mean the PC is on its way out.

By CheckDisk you mean chkdsk?  with /f or /p?  or do you mean with /r?  Any bad sectors that /r fails to fix and was reported as such but went by on the screen output in previous runs, those affected files or folders will be corrupt.  Did you capture the error output of those chkdsk /r, not likely eh?  
It's why I detest chkdsk /r option as lowsy for dealing with bad sectors, it gives up reading too easy so it sets bad sectors aside forever alright but you lose the data in those sectors!   You're then expected to recover said files from backup or replace.  It's why I recommend HDDRegenerator or SpinRite or HDat2 for dealing with bad block disk errors.

maybe it changed the proxy settings :  http://forums.malwarebytes.org/index.php?showtopic=54899

Wireless Zero Configuration is running. I'll check the other after I reload the image. I used chkdsk /r & no errors were detected. It is a PATA machine. My XP disks have SP1 or SP1a. They should still load but may have to activate Windows when done. There are no proxy servers.The repair installation freezes on boot with the Windows page. Rebooting at that point by power interruption or by holding the start button gives a momentary BSOD & another reboot. It will complete a clean install, but I couldn't find new drivers for the controller. The MEDION website gives a blank page for drivers. I tried DriverAgent, but it didn't work. This laptop has a small control panel on each side of the keyboard. Neither panel works. The on/off for the WLAN is on the right panel, but the system tray showed it working, just no available networks.

I turned on Wireless Autoconfig. It uses an app called Prism by Intersil to run WLAN. The Windows app does not scan without it. Prism scans the channels but sees nothing.

for running  a repair, i suggets to integrate sp3 into the install cd  :
http://www.howtohaven.com/system/slipstream-xp-service-pack-3.shtml

also - i suggest to use the Lan, not WLan

I ran an upgrade installation to XP Pro SP3. It froze but completed after power interrupt. It did not fix the WLAN problem. The owner has no LAN available where she uses the laptop, so WLAN is essential.

i mean - use the lan to get it repaired (downloads, etc..)
>>   It froze but completed after power interrupt.   <<   overheating?  then install speedfan : http://www.almico.com/speedfan.php      

otherwise post the laptop model

It wasn't overheating. It is a Medion MD 2900. They were made exclusively for Aldi's food stores as a promotion. The Medion website gives a blank page when you enter the model number to get drivers. I found the Prism utility through DriverAgent. I tried running without the utility, but Windows utility did the same.

A USB dongle works. They will just have to get used to it.