I can't make a recommendation, but I'll offer some comments in the hope that they may be of some help.
My first port of call in pricing non-Apple PCs is Dell's website. Their prices give a guideline, even if you choose something from a different company, such as Lenovo (IBM's former PC business) whose notebooks still seem well regarded by people I trust.
| intel graphics _or_ in rare cases , nVidia GO FIND POWER DRAW
For web use (and word processing and spreadsheets and computer science assignments and ...) any graphics chipset is probably going to be just fine. Areas I know that graphics chipsets matter for are:
i. games, because performance matters (and I'm no game player and can't help)
ii. non-Windows operating systems such as Linux, where not all chipsets are equally well supported
| preferably 1400x900 or better resolution (not necessary if it's reely cheep)
Widescreen models are very popular now; you might not get 1400x900 depending upon your price limit, but something respectable should be OK.
You don't say what size of PC screen your son wants? I prefer smaller screens because the notebooks are physically smaller and lighter, but I expect to mostly use an external monitor and only use a notebook screen when travelling.
| 2 hd slots would be nice, but unnecessary
These days I would not worry about that so much: adding external storage (typically via USB) is easy and helps avoid loss of all data if something bad happens to the notebook PC.
| ability to have 4GB ram
You might have to settle for 2GB, and practically, 3GB may be the effective maximum even for a system with 4GB installed. The reason why is rather technical, but is explained here: Ask Dan: What's with the 3Gb memory barrier?
| as much cache as possible (looks like 4Mb for intel, 1Mb for amd)
Mmm ... dunno how important this is. I would not fret about it greatly. Maybe it matters for games, or maybe not.
My last work PC's CPU was almost never busy; my current (Mac) desktop is only busy when Photoshop is handling something big. And that's a several year old box slower than most anything (including notebooks) that you can buy now.
| lowest minimum processor speed
For battery life? I think it's a pretty standard feature to be able to run the processor at lower speed on battery. I'd have this down the priority list, in part because finding the data about a particular machine that you're interested in may be difficult.
| no bundled OS (if possible)
Hard. If you make this a requirement, your choices will be reduced.
Why is your son looking for this? If it's because he plans to run Linux, then I suggest the requirements list be changed to be a cost-effective notebook known to run Linux well. (Speaking as one who's run various non-Windows operating systems for one reason or another on PCs since about 1990, struggling with hardware for which there is no or poor non-Windows support gets old fast.)
I'm as much a fan as anyone of not paying Microsoft money, but let's be practical: if it's cheaper to buy hardware /and/ pay Microsoft than it is to buy similar hardware otherwise, Just Do It.
| atheros chipset? (probably not going to happen. intel 2200, 2915, 3945, etc should be fine)
This is wireless, and pretty much anything will work IF the operating system supplied with the machine is used, otherwise, yes, this becomes a point to consider.
| ability to replace cd with battery (really really want this)
I haven't tracked how many notebooks allow this, but I know some do or used to. If the feature isn't available, suspending, swapping the battery and resuming is a workaround. (But suspend support under Linux et al is less good than Windows, unless it has improved very recently.)
| I'd like to see reliability and minimal cost.
Reliability and notebooks aren't exactly boon companions. Until the recent (last year or so?) price drops in notebooks it made sense to get an extended warranty (from the vendor, NOT a third party) but now ... it's less clear.
I would still be wanting to buy a "name" product backed by a competent service organisation: repairing notebooks is much harder than replacing failed components in a desktop PC.
Lastly, as a general guideline in the PC business: the very cheapest products are engineered down to that cost. A rung or two up from the bottom of the ladder is usually a better bet for reliability and performance.
P.S. Quickly looking at Dell's site, I see that some models don't come with DVD writers. I'd be looking to have a DVD writer, I think. CDs are pretty small for backup these days, and DVD blanks are nearly as cheap (or might be as cheap by now) as CD blanks.