|"One option is to plug into my phone line, but I do not want to tie up the line while I do the updates."|
You must also have the option from your ISP of their services via a dial-up modem connection. When you connect via a DSL or ADSL ISP (a telephone line) , you usually have that option, but I've never heard of that being an option for a cable high speed ISP (Internet Service Provider).
"PCMCIA Ethernet adapter"
Apparently your model's PCMCIA slot supports Cardbus (32 bit cards).
Product Specifications - DOES mention Cardbus
One (1) Type II PC Card slot with support for 32-bit CardBus
You can use any Type II PCMCIA network adapter (a.k.a. PC CARD) that supports Cardbus (which is the vast majority if not all of the new ones), wired or wireless, or you can use any 16bit PCMCIA network card (Cardbus is NOT specified) , which you are much more likely to find used rather than new, and there may be no new wireless ones (certainly not wireless N ones in any case), only wired ones.
However, which operating system are you using on this laptop?
There may only be support for using the adapter in 2000 and up, unless you use an older model, which you may only find used.
If you have a router between your computer and the internet connection (the standalone high speed cable modem, or the combo router / high speed modem), you can connect to that by using a network cable in any case (a wired connection) if the PCMCIA adapter is a wired one (has a RJ45 jack), or if the router is also wireless, with a wireless PCMCIA adapter.
NOTE that a wired 10/100mbps or wired 10/100/1000mbps (gigabit) adapter connection yields you the capability of a faster internet max speed than a wireless G or wireless B adapter, if the router also supports that. Wireless N adapters have a similar capability compared to a wired 10/100/1000mbps (gigabit) adapter, in 1000mbps mode, regarding that, if your router supports that.
The max speed on the internet capability depends on what the ISP's package you are paying for supports.
"Ethernet to USB cable from router to USB port;"
According to the above specs, you have only one built in USB port. It's probably NOT a good idea to use that for this purpose. Many people that have laptops use a USB hub, but USB ports in a hub connected to a built in USB port DO NOT work for many things.
You can get a USB data transfer cable - it has circuits between the two ends that allows you to transfer data between two computers using USB ports. You could transfer program installation downloads etc. from another computer you downloaded that to, however, that won't help if what you want to do is get Windows updates.
As far as I know, there is no such thing as a cable that has a USB connector on one end and a RJ45 connector on the other, even one with circuitry in between, that will allow you to connect to a router and the internet.
There are USB network adapters, wired and wireless, but you have only one built in USB port, not a good idea to tie that up, and it supports only USB 1.0 or 1.1, not USB 2.0 - that would be a bottleneck to your max speed on the internet, if the ISP's plan you pay for supports higher max speeds - you don't have that limitation with a PCMCIA (a.k.a. PC CARD) adapter .