They never did, what they changed was the connector on the logic board, so you can only use their proprietary cables, and that was with the 2011 models. Technically before that they did have odd cables. One end would be your standard 3.5" SATA, the other would be a 2.5" SATA, but you could probably find something like that on the likes of Monoprice. With the Late 2009 models, IIRC, they started doing away with stick on temp sensors and started having drives loaded with custom firmwares to give temp readings. In the 2011 models this cable was done away with and it was apparently being sent via the SATA data connection or maybe there was some other sensor mounted under the drive mount I never noticed.
Now, since I'm too lazy to make a second post, the rest is addressed to the OP:
The old white iMacs used one really long SATA data cable and then there was another power cable routed separately. It would be just a plain SATA drive though. Doesn't look like SATA 2 really made it to market until around 2010, and even if it had been out a bit earlier, given the 8-12 months that that specific model had likely been in development, testing, and ramp up production, SATA 2 would have had to of come out around maybe late 2004, and SATA itself wasn't established until 2003.
One word of caution, is that it's nigh on impossible to replace the HDD in those models without removing the logic board first. It can be done, but naturally there are a few key parts that are in obnoxious places. Also, make sure to do something very relaxing, like meditate or whatever, before starting in on that. Having read instructions on how to open those units and actually doing it are very different things, and then you get to experience the joys of the EMI shield and trying to get that off without ripping it to shreds, but not before you have to blindly disconnect the webcam cable (and reconnecting it later is a real treat). It's all but guaranteed you'll bend the retaining clips and the front bezel will never go back on right. The EMI shield can also give some nasty paper cuts if you're not careful. The next bit of fun is getting the screws holding the display panel in, out, which is a slightly easier task than getting them back in later. You'll also probably just want to use some scotch tape or something to hold the temp sensor in place on the new drive. Don't trust the adhesive to last long-term, even if it feels solid when you put the drive in.
The white iMacs starting with the iMac G5 iSight model, were an absolute nightmare to work on. Fortunately they abandoned that design rather quickly. You may really want to consider paying someone to do this for you. Any later model, and it wouldn't be that big a deal, but this one is a righteous PITA.