My house is completely wired with coaxial cable (home runs). Does any
body make a "coaxial cable router?"
Let me be more specific. Signals from the wireless router in my house
do not go more than about 35 to 50 feet, which makes it almost useless
for me; so what I would like to do is attach my cable modem to a
"coaxial cable router", then attach the existing coaxial cables going
to the rooms where I have my computers to that router, to then in each
room attach some sort of a coaxial cable to RJ 49 converter between
the computer and the cable termination, and in this way duplicate what
the wireless router was supposed to do for me, but didn't.
Does anything like that exist? and if not why not?

Very frustrated 48

this is therotically possible, but you would not be able to utilize
the existing cable as you would need a separate run from the router to
each computer.  also while coax can and is used for networking i think
you would find the cost of using it in your home prohibitive.  good
idea, but i think your best bet would be to run cat5 cables from a
non-wireless router.  i dont know much about wireless networking
technology but i think there are ways to boost the signal im just not
sure of any short of buying a more powerful wireless router

Coax or BNC cable was used in the 90's for building networks (It is
and was known as 10Base2)  the cable needs to be 50 ohms cable and
needs to have a terminator at both ends and one end needs to be
grounded , your ( i suppose) TV cable can be used for this if you
don't mind a little preformance loss and network equipment can still
be found in a lot of second hand computer equipment places (3Com brand
is most commonly found) also you will need network cards , bnc crimp
connectors , a pair of crimp plyers ,T connectors and -depending on
the distance you are going to cover- repeaters

Also be aware the max throughput of BNC cable is 10 Mbit 

A company you can try for second hand or refurbished equipment is 
www.cxtec.com  

CXtec
5404 S. Bay Rd.
Syracuse, NY 13221-4799
Phone-315.476.3000
Fax-315.455.1800

Hi iamjustcurious-ga,

 Since the others have pretty much covered the options on using coaxial,
Here are my suggestions to get most out of your wireless network:
i) You could use directional antennas to improve the range of the wireless
netowork in some cases.
ii) You could also try a passive repeater approach(could tee of the existing
coaxial(at both ends) to connect to a small form factor 2.4GHz antenna),
since the antenna's will be tuned it should not cause enough concern of
radiation if used with existing cable service under 1GHz(if you are using
the coaxial for digital satellite it could cause interference/radiation in
the 1-2GHz being used).  You might think about upgrading your existing splitter
for a satellite one(upto 2GHz range) and also think about coupling the
accesspoint router through an RF amplifier(may not be necessary).
iii) Use multiple access points(use the primary router in the point to multi
point, and all the rest could serve the local coverage.

Regards
ldavinci-ga

I'm curious to know why the range of your existing hardware is so short. 

From <http://www.vicomsoft.com/knowledge/reference/wireless1.html#6>

"Each access point has a finite range within which a wireless
connection can be maintained between the client computer and the
access point. The actual distance varies depending upon the
environment; manufacturers typically state both indoor and outdoor
ranges to give a reasonable indication of reliable performance. Also
it should be noted that when operating at the limits of range the
performance may drop, as the quality of connection deteriorates and
the system compensates.

Typical indoor ranges are 150-300 feet, but can be shorter if the
building construction interferes with radio transmissions. Longer
ranges are possible, but performance will degrade with distance.

Outdoor ranges are quoted up to 1000 feet, but again this depends upon
the environment.

There are ways to extend the basic operating range of Wireless
communications, by using more than a single access point or using a
wireless relay /extension point."

What version of 802.11 is your current router? Instead of spending
money to make use of your existing coax (you didn't mention if it was
currently active with any TV or Sat signals), why not invest in an
upgrade of your wireless router/access point? And if the construction
of your building prohibits a greater range, maybe you can invest in
some range extenders.

Personally, I would not go with range extenders / antenna boosters
etc. because they invite problems like more latency and slower speeds.

I believe there is no router yet with a coax connector, but there was
talk of an adapter to allow a bridge over to coax.  However, this is
so similar to other types of bridges I would choose a more time tested
option.

One such option (this is my favorite) is the HomePlug powerline
adapter.  I use the Netgear XE102 Powerline Adapter and have had great
success.  If you can get it from a shop like Best Buy or Fry's you can
take it back if it doesn't work.

These are going for about $50 each lately and if you can use them like
a wired network if you connect directly to your computer (very
reliable), or if you gotta have wireless then get another router and
connect it to the adapter in the place where you have bad reception.

Trying to go coax at this time might be like reinventing the wheel. 
With wirless everyone is fighting for airwaves.  My bets are HomePlug
or combinations of HomePlug and wireless.

Are you using 802.11a ? It is normal for this standard to only work up
to 25ft. The range of frequencies limits the distance. I would suggest
a "downgrade" to 802.11b or 802.11g. There is no upgrade past 802.11a.
*02.11g would be the best solution.