There are several layers here (literally and abstractly). Some disentanglement is in order.
At the lowest layer, the wire, there are only changing voltages running around. What they mean is the responsibility of the next layer up (or down as your views on the Satanic qualities of network mysteries may incline). That's where Ethernet lives. Software, assisted by hardware in the interface, produces and interprets those voltage pulses in such a way (we finesse the details here to save sanity and my fingers) that it becomes possible to send bits reliably from one Ethernet node to another.
That's where the 10/100/1000 spec comes in. It's how fast the bits get swapped around. Higher (or lower) layers establish communication between nodes ("I'd like to talk to node xx.yy.zz", "I'm here, go ahead", ...) and such things as data formats (eg, images of this kind are organized for sending receiving this way, text files another, word .doc files still another, ...) and so on.
The classic layer stack was specified by the ISO many years ago (seven layers), but the most widely used (TCP/IP on the Internet) doesn't quite match the way the ISO broke out the layers. Whichever abstract protocol stack model you love, in actual working equipment every layer takes what it's given, packages it up as required and hands it to the next (or, on receipt, strips off the encapsulation from the previous layer and hands it on), and every one of those steps takes time and some processing.
As a result, neither you nor anyone will EVER see the raw speed of the underlying medium appear where you work, with Web data, word processing data, image data, ... Whether the reduced speed you see is 'reasonable' is another question.
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your situation
If you have a poorly implemented protocol stack, it likely won't be reasonable (by most valuer of reasonable), but changing the Ethernet protocol stack in your machine is advanced surgery (though bloodless unless something Goes Wrong) and is the sort of thing the folks who put it all together for your machine are in the best position to do. With a well implemented stack, 100mbs Ethernet is very very fast; Web pages display with snap and sparkle (assuming, of course a large pipe to the Net). With layers of not necessarily very well thought out stuff (including operating system interactions) on top of the Ethernet wiring, things can bog down.
Check for viruses and spyware (either can slow down most anything) and perhaps defragment your hard disk(s), and check for read errors from the disk controller (if your disk is failing, most things will be dicey and slow too, but your system will be in extremis by the time you notice much), and if all seems well locally, talk to the vendor about it. There may be a 'patch' (a rewritten chunk of stuff) which might help. Which brings up a question -- are you using the latest (ie, most up to date release) versions of your operating system, and components. If you're not, vendor help is likely to be 'limited' and less than enthusiastic.
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Gigabit Ethernet
There's a hard limit here. Most likely. If you have a PCI bus machine, you will (or have) encountered it. Gigabit Ethernet is faster than the PCI bus (mostly, in most situations on most hardware) and you will be running crippled Gigabit Ethernet if you try. The Ethernet part may be working perfectly (and will be right quick), but it will spend a lot of time waiting for your system to get it the data, or to read it once delivered. There's nothing to be done (faster CPU etc) since the bus is the limiting factor.
Newer motherboards are coming with the PCI-express bus, which is quite different despite the similar name, and is much much faster. Not very many of these, and not very many add-on cards for them either, as yet. But even so, there are other bottlenecks.
Let's assume you've one of these motherboards, a PCI-e Gigabit Ethernet card, and that the hardware (and software drivers) all work perfectly. If your chipset can't get the data to and from the bus as fast as the bus needs it, there will still be a hard limit. A few months ago, the nVidia 4 chipset was about the only one that could move data fast enough to let Gigabit Ethernet run at full speed continuously, assuming you had that much data to move. Things are constantly changing and I expect, without actually looking, that there are several more out by now. If not now, soon.
Keep in mind that, aside from all the other bleeding edge issues noted, this is indeed all bleeding edge stuff. Unless you really need it, you're best off taking a pass for the moment. Besides which, there are very few existing situations which require Gigabit Ethernet. Large database replication perhaps (100s of metgabyte of valuable data (some of which may be correct), which is being served to the Web in 10s of 1000s of sessions simultaneously and must now be backed up for safety, or scientific data analysis (the amount of data generated by a single run of a particle accelerator is astonishing; it's rather like trying to take a sip of water at the bottom of Niagara Falls, likely to choke you on volume alone, regardless of what plans you'd had), or weather modeling or ... Of course, if you're responsible for getting all those eavesdropped conversations onto hard disk they can be analyzed by state of the art semantic analysis software, you might be in desperate need. Your monster RAID farm might be best set up with a fiberoptic Gigabit Ethernet connection to the data source(s), and you'll probably be able to find the funding rather easily.
Unless you're doing something like one of these, Gigabit Ethernet isn't going to be much help with your troubles. They aren't fundamentally speed starvation. But, you'll have all that expensive fun on the bleeding edge as a bonus if you go down that blind alley. Not to be sniffed at, that.