All motherboards come with and have a BIOS. Its needed for a PC to start.
Your system is older. It's socket 478, DDR(1), AGP, IDE, etc. Those are all at dead ends and not cost effective to upgrade for.
The PSU is standard. It's not proprietary. Dell stopped that with the Dimension 4100 (Pentium III era) being the last to have a proprietary PSU.
The bad news...
Dell obviously still wanted something proprietary, so it's now the motherboard, sort of. What I mean by sort of is that it's really standard, but the case/motherboard are fit together in a proprietary way, meaning a new motherboard means a new case, and with a new motherboard, you'll need new RAM, a new CPU, and GPU, and then surely that Dell PSU won't be enough. In other words, it's possible, but you're basically going to be needing a new system anyway, so why kill the Dell? The old HDD WILL be slower and yes it WILL make a difference using an IDE drive versus a new SATA one. The only thing salvageable might be a sound card if any (the GX260 should have onboard) or the CD/DVD-Rom drive, but those are only $30.
I was in the same boat last year. I had a GX270 and upgraded it over time (PSU, CPU, GPU, added RAM, and so on), and while I don't regret it, since it came in steps and I made SURE to get it cheap, if you're doing it all in one step and will go retail (I went second-hand eBay), it's not worth it in my opinion. It won't be cost effective. Keep the Dell as a basic machine and get a new one for games. Hardware is cheap these days and even budget machines do well. They won't be as good, of course, and will become obsolete quickly (but what doesn't, and who cares?), but even a modern budget PC will smoke that Dell, and it doesn't take the best to run Call of Duty 4. If you decide to buy a new build, give a budget and others can make suggestions.