Hi ydyjdwp
I think an add-on ethernet card is still a good choice. Shouldn't cost more than $10 (usd). If you haven't a good cheap card at a nearby electronics store, check your local craigslist computer items - there might be an older 10/100 card for about $5.
Most DSL ISPs have their authenication handled by the "DSL modem" that they provide (or if purchased by the user, the ISP 'login' is handled in the hardware ... that account info is entered into to the device during setup]. The gist of this: there's very little software compatibility to worry about. Any OS, any browser - should work. So long as the ethernet card in the PC works, you're good to go.
If the PC is meant for light use, and much of that Internet oriented, I'd recommend trying a lighter version of Linux for it. It's hard to secure Windows 98 on the Internet anymore -- (certainly not cheaply, as most of the free-for-personal-use antimalware programs no longer support win98). Most Linux distros come with a default software firewall, and many can detect and install drivers for ethernet cards old enough to be compatible with your Dimension 350. Firefox & Open Office are commonly installed by default as well.
To test-run Linux (without having to install anything), from a more recent & capable PC create Linux Live CD . . . Knoppix is a good choice as a trial ---
http://www.knopper.net/knoppix/index-en.html --- It would be best if the old Dimension has over 256mb of system memory (for somewhat comfortable performance), but Knoppix can run on as little as a 486 with 128mb of memory [even less, if the office programs aren't needed].
A good light version of Linux for older machines is Xubuntu (a lighter variation of Ubuntu) ---
http://www.ubuntu.com/products/whatisubuntu/xubuntu ---
The full Ubuntu is even easier to use, and offers much more built-in software, but generally needs 384mb or better system memory and 4gb of hard drive space ---
http://www.ubuntu.com/products/whati...desktopedition ---
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Other options:
1) A dual-boot system: If the hard drive is big enough, having both Linux and Win98 are possible. The ethernet adapter could be disabled on the Win98 side, so that all Internet access occurs in Linux. (Internet safety in Linux, old Windows software/games would run in Win98)
2) Keep Win98 installed on the hard drive, but boot into Linux via a Live CD when Internet access is desired.
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Might as well have a bit of fun with the project ... perhaps even pickup a spare hard drive for free from a friends garage ... that old hardware might get spotty not so far down the road (you might be seeing it again in the not-so-distant-future).
Best of luck
. . . Gary