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The motherboard is an ASUS CUSL2-C
Intel 815EP chipset
The CPU is a Celeron II 1G
I want to upgrade to a Celeron III 1.3G
Question: do I need to change the motherboard?

Because I once wanted to build a machine with a third-generation Celeron, I can tell you without any doubt: there is no way unless you add an adapter card. Although the CUSL-C provides 1.5V, and there is a 1.5V version of the third-generation Celeron (there is also a 1.475V one), because the chipset is different, it still won't work even if you install it.
Also, for your first purely technical question, I'm afraid not many people can answer it directly; they'd have to look up the documentation too. Since you know the motherboard maker and model so clearly, this little matter shouldn't be able to stump you, right?

Hehe...
Is there a Celeron III? I think what you mean is the Tualatin Celeron II, right?
At present, all Socket 370 motherboards cannot directly support the Tualatin core; you'll run into a failure-to-boot situation. Besides the different voltage, the processor signals are also somewhat different. But recently I heard that Powerleap has released a Socket 370 adapter card that supports the Tualatin core. Through it, we can use Tualatin-core processors on our existing motherboards. However, Intel seems never to have certified any adapter card, because it wants users to upgrade their systems faster. But this really is a good solution.

The following is quoted from iceboy's post on 2003-11-16 17:42:46:
Hehe...
Is there such a thing as a Celeron III ? I think you mean the Tualatin Celeron II, right?
At present, none of the Socket 370 motherboards can directly support the Tualatin core; you would run into a failure-to-boot situation. Besides the different voltage, the processor signals are also somewhat different. But recently I heard that Powerleap has released a Socket 370 adapter card that supports the Tualatin core. Through it, we can use Tualatin-core processors on our existing motherboards. However, Intel seems never to have certified any adapter card, because it wants users to upgrade their systems faster. But this really is a good solution.

Couldn't be more right. But adapter cards aren't cheap either. If your motherboard has been in use for quite a while, you could also consider replacing it with an ASUS TUSL series motherboard (if there are still any new ones). Starting with T means it supports Tualatin Celeron. Also, for some improved chipsets such as INTEL's 810T, 815ET, 815EPT, VIA's 694T, and SIS's 635T, the added T at the end likewise means support for the Tualatin third-generation Celeron.
But from my experience, these boards supporting the third-generation Celeron from first- and second-tier makers like ASUS, MSI, Gigabyte, and ECS have long since been discontinued, and the dealers' stock in the computer market should probably all be sold out too. (Last time I searched the entire computer market in my area and still couldn't find a single board, 55555.) What remains is stuff made by third-rate manufacturers, and neither the quality nor the after-sales service can be effectively guaranteed. The workmanship is poor; for example, some northbridge chips don't even have a heatsink. But that doesn't matter much, so forget that. What's outrageous is that the lettering on the chips is actually blurry, which is just too much . Also, in order to cut costs, these manufacturers' designs can be summed up in one sentence: "reference design on top of reference design." I looked at seven or eight brands; aside from the color and brand being different, the entire board's circuit design was practically "twins." Also, this stuff is sold one board fewer each time one is sold. If it breaks and there's no replacement stock, then what? Do you think the seller will compensate you out of pocket? Hehehe~~
I'm not advertising for INTEL. I just think your Celeron 1G is already fast enough. Simply upgrading the CPU won't make much difference. Sit tight, be patient, P4 is already beckoning to you~~~

1. Truly an expert! I admire you immensely, but I heard that adding a 370-to-370 Tualatin adapter card is enough. But Tualatin Celerons only go up to 1.3G at most, right? Are there any Tualatin Celerons above 1.3G? How much would I need to invest in total for a Tualatin Celeron 1.3G plus a 370-to-370 Tualatin adapter card?
2. What's the highest clock speed for CII? What's the highest clock speed for CIII?
3. Early this morning I couldn't wait and removed a Tualatin Celeron 1.3G from a friend's machine and installed it in mine. As a result, as soon as I powered on, the case speaker kept sounding nonstop like an ambulance. I hurriedly removed it again. Good thing I didn't burn out my friend's CPU, hehe.

The following is quoted from pxtttc's post on 2003-11-16 7:12:21:
The motherboard is an ASUS CUSL2-C
Intel 815EP chipset
The CPU is a Celeron II 1G
I want to upgrade to a Celeron Ⅲ1.3G
Question: do I need to change the motherboard? 

You can go to ASUS's homepage and see whether the CUSL2-C can support CIII after a BIOS upgrade. Generally speaking, 815 can support CIII, and ASUS handles this especially well in that respect. Or you can leave a message on ASUS's forum.
There is now a kind of adapter card, 370 to 370, which can make 810 or 815 support CIII. You can also check the computer market; it's about 30 or so.

Switch to XP instead

The following is quoted from DOX's post on 2003-11-18 8:08:48:
换XP吧

What do you mean?