The Dell was actually pretty much silent with the exception of the aforementioned HDD seek noise. I am not sure how quiet it would remain when the intake fan ramps up as temperatures rise.
Operandi is absolutely correct in stating that building a quiet system is quite easy when one is not using high-performance hardware. The Dell I set up had one high-end piece in it, which was the processor- and, due to the simple (cheap) aluminum heatsink and low-spinning front fan, it ran extremely hot even at moderate loading. Granted the P4 Prescotts are rated for a higher max temp than the A64s, I would still feel uncomfortable using the Dell under full CPU load for hours on end during the summer, sans AC. I am not sure how well a high-end video card would fare in the Dell case, considering how lacking it is in general airflow (as I stated, it is well-ventillated in terms of having adequate air entry and escape routes, but there is only so much one can do with just two fans in the entire system- which might become a problem when adding in another significant heat-producer such as a modern GPU).
Bottom line, IMO- the Dell will suffice if you do not regularly place a lot of stress on the system and/or do not run it for long periods of time with high ambient temperatures. You stated in your original post that you were after "quiet operation, not performance." If this is the case, and you can get a good deal on it, a Dell would suit your needs.
If you have the time and know-how, though, a socket 754 Sempron in any halfway decent case with low-flow fans and a soft-mounted HDD will give you all of the quiet of the Dell with significantly less heat generated.
To give you an example:
Socket 754 mobo w/integrated video: $65
Sempron 2800+: $65
Case: $40
PSU: $40
HDD: $40 (80GB)
Ram: $35 (512mb)
DVD Burner: $40
Windows XP Home OEM: $70
Total: ~$400
In comparison, the E510 with nearly identical specs that my friend purchased cost a total of ~$550 shipped with a 19" analog LCD monitor. You can buy a 19" LCD w/DVI for <$250 ; a 17" DVI LCD can be gotten for <$200.
So, you would probably spend $50-150 more on a hand-rolled rig if you include the price of the monitor. However, even though the specs would be similar to the Dell's, your custom system would most likely have a superior PSU and a non-proprietary case that could be used for future builds. The Dell on the other hand would come with a better processor and a dedicated GPU (ATI X1300), but if you do not need the high performance, a Sempron will serve you just fine, and be much cooler (and therefore require much less airflow, and hence, produce less noise); integrated video is fine for 2D and old-school 3D games, and an add-in GPU can be had for <$40, which might be useful if you want DVI, as no socket 754 mobos support DVI-out to my knowledge.
You can see there is no clear answer- but you definitely can build a system just as quiet as the Dells for a similar price. Whether it is worth your time, and whether you will really benefit from it is up to you.