Practically speaking there is no 6-8 year old computer that can be upgraded to capture HDV video from your HC7. It's not the video card as much as it is the requirements that HD editing has for processor speed, memory and hard drive speed.
Here's the minimum requirements to be able to capture HDV footage using Adobe's Premiere Elements, an entry level HD editing package:
Intel® Pentium® 4 or Celeron® 1.7GHz (or compatible) processor;
(Pentium 4 3GHz processor required for HD or Blu-ray)
Microsoft® Windows® XP with Service Pack 2 or Windows Vista®
For Windows XP: 512MB of RAM (1GB required for HD or Blu-ray)
For Windows Vista: 1GB of RAM (2GB required for HD or Blu-ray)
4.5GB of available hard-disk space
Color monitor with 16-bit color video card
1,024x768 monitor resolution at 96dpi or less
Microsoft DirectX 9 or 10 compatible sound and display driver
DVD-ROM drive (compatible DVD burner required to burn DVDs; compatible Blu-ray burner required to burn Blu-ray Discs)
DV/i.LINK/FireWire/IEEE 1394 interface to connect a Digital 8 or DV camcorder, or a USB2 interface to connect a DV-via-USB-compatible DV camcorder (other video devices supported via the Media Downloader)
They don't list it but you'll capture video more easily with a 7200RPM drive also if your BIOS will support it. But it likely won't without a third party software add-on due to the age of your computer. And if you can get the bios to recognize all of the drive, you'll also need an UltraDMA add on controller most likely since your existing drive controller won't be able to handle the increased throughput.
Another limitation you'll likely run into with a machine that old is that it your motherobard likely won't support a faster processor. Or if it will upgrade, probably not a fast enough processor. Not to mention that the chip socket might not be compatible with any of today's processors.
Swapping your motherboard might be an option if you have an ATX-style case. If it's an AT case you're going to find your options are really limited...If it's also a proprietary design by one of the big manufacturers you may also find that options are limited - they have a nasty way of being just non-standard enough so you can't swap motherboards.
If you want to edit HDV, it might be cheaper to buy a new fast machine. I haven't priced them lately but I'm sure that you can get one under $1000 that will meet all your needs.
I have a 5yr. old Sony VAIO, The "V" in VAIO stands for Video so it's a machine that was built to edit video. It's too slow and not upgradeable to allow it to be used for HD editing. So it's now my Internet box, I'm typing this on it...
However, your HC7 does have the capability to output in SD so if you can upgrade your old computer to meet the minimum specs, you'll still be able to capture and edit SD video. And you can save your HDV footage on the original tapes for when get a faster machine.
Some software options: Adobe Elements at $100, Sony Vegas Movie Studio Platinum for $129, and Pinnacle Studio at around $100. All will edit in SD now and later in HDV.
What type of graphics does your motherboard support - SVGA, AGP or PCI? I don't think anyone sells a video card that's not AGP or better. Except maybe on eBay.