On this case since you are not able to detect the Solid State Drive I suggest you to move the Solid State Drive to the SATA port 0 or 1 and try to select the AHCI option in your BIOS.
You can also try to update the BIOS of your system and update the SATA drivers of the SATA controller.
Another recommendation is to change the SATA and power cables for the Solid State Drive and try again.
I assume SATA Mode of "SATA" means "IDE" or "Compatibility" mode? Most likely your storage controller's driver is not integrated with the Migration Tool.
The other possible workaround is if you have another computer avaliable and you might have better luck.
The Data Migration Software Help document can be downloaded here:
According to this document, this tool was never tested in the Windows XP SP2 environment, which is what is on your HDD according to your post. It was tested in XP SP3. So very generally, that is probably why it doesn't work for you. As I recall, there was a significant difference between XP SP2 and XP SP3.
Your Dell PC has the Intel 925X Express chipset, with an ICH6R SATA interface. You might want to try updating the chipset software from the page below:
You must choose your OS/Version of Windows to get the appropriate files. Who knows what INF files and drivers Dell has on your PC.
Unfortunately, I cannot guarantee that updating these files will fix your problem. The Help document in the first link describes a way to create a System Report to send to Intel support to assist in figuring out your problem.
I've heard of people being unable to run the SSD Toolbox in Windows XP, and since you can there may be hope for you yet.