I need to make a real mobile base for my table saw. I don't want this
to be overly long but I think some background is needed.

My 'shop' is a very crowded garage that I share with two cars. And if
I want to stay married, which is the plan, there WILL be two cars in
the garage as much as possible.

That said, I have precious little space, really for my tools. I own a
smaller table saw (Delta 36-600) which doesn't know what it want to be
when it grows up. It has a smaller table like a benchtop but sits on
legs like a contractors saw . It is a belt drive (using a laughably
small belt) which sits under the table, so I can push the whole thing
against the wall--which I need to do. It's not the best saw in the
world; not the worst saw in the world. It is quite noisy but it does
what I need for it to do and I am happy enough with it.

Okay, that said, I currently have it on a crude 3/4" plywood base with
crappy wheels. I knew it was wrong when I made it but I just wanted to
hurry up and get it together. It is starting to become a realpain in
the posterior lately, however, for several reasons. Mostly because the
base simply sucks. Also because of the $#^$*%^!! drain in the middle
of the garage floor. No matter where I position the saw, that
$#^$*%^!! slope kills me. I need to put wedges under one of the wheels
and I know that just ain't no good.

Soooo.....I figure I want to make a new mobile ase but why stop there?
I have precious little room, so why not build a cabinet to replace the
legs? I want to learn how to make cabinets anyway, so here is a good
reason to start learning.

Next, I figure I could finally find a use for those two old trailer
jacks on wheels I have and could connect them to the base. When I
wheel the saw out, I could lower some levelers in the base and flip the
trailer wheels out of the way. That, combined with the cabinet I want
to build, would make for a very heavy, very firm and very stable base.

I feel I will be creating something that makes a lot of things better,
but I am still left with the noise issue. The earmuffs solve the
problem for me but if anybody else in the family is even near the
garage, they, well, let's say they just let me know about
it--especially the silly cat. I think if he is there just one more
time, ALL of his hair will finally fall out.

I am wondering if it would be feasible to lay a piece of indoor-outdoor
carpeting on the top of the cabinet and set the saw on it? Would that
have any noise dampening effect? Or would I just be courting disaster
for some reason? Do you think it would have any effect on vibration?
One would suspect it should work okay but when I start think' like
this, it usually turns out the answer is completely the opposite of
what I think.

Any thoughts?

My 'shop' is a very crowded garage that I share with two
cars.

I have an ONE car garage, and my car is parking inside it along with my
standard contractor-type table saw with cast-iron table top, and I will
have a folding outfeed table when I am all done. Seem like your garge
workshop is not that small after all. You should have no problem
fitting everything in it.

Also because of the $#^$*%^!! drain in the middle of
the garage floor. No matter where I position the saw,
that $#^$*%^!! slope kills me. I need to put wedges
under one of the wheels and I know that just ain't
no good.

I have a similar problem in my garage floor. Mine has too many peaks
and valleys on the floor. I intend to level four small spots on the
floor very level and smooth, and then position the wheels of the table
saw mobile base right on the spots.

Soooo.....I figure I want to make a new mobile ase but
why stop there? I have precious little room, so why not
build a cabinet to replace the legs?

I am planning to do exactly the same thing as what you want to do. I
have got all the materials ready in my garage. I need to wait for next
spring when the weather is good (my garage is not heated and I don't
have any portable heater and I am too busy right now).

I will make the under table-saw cabinet as big as the table saw top;
then it will not take more space than it is taking up now. I will put
table-saw related tools/supplies/small-jigs/push-sticks in the cabinet.

The cabinet will also be the mounting-surface for duct for dust
collection to collect dust from the bottom of the table saw. I still
have not figured out how to mount a hood above the saw blade to collect
dust from above. But I have a feeling that the cabinet will again be
the place to mount any dust collecting hose over the saw blade.

Next, I figure I could finally find a use for those two
old trailer jacks on wheels I have and could connect them
to the base. When I wheel the saw out, I could lower
some levelers in the base and flip the trailer wheels
out of the way. That, combined with the cabinet I want
to build, would make for a very heavy, very firm and
very stable base.

Sound like a plan.

As for mine, I will put four large locking caster wheels to make the
cabinet mobile. Yours probably will be more stable. But the locking
wheels should be stable enough for me.

... The earmuffs solve the problem for me but if anybody
else in the family is even near the garage, they, well,
let's say they just let me know about it...

Not sure why this can be a problem for your family members. Mine is a
detached garage. When I use my table saw to cut wood, my family members
don't notice a thing (as long as the garage door is closed), and my
house and my garge are not that well insulated either. May be you want
to ask your family members to see if noise is really an issue or not.
If this is not an issue, you don't need to do a thing on this.

I am wondering if it would be feasible to lay a piece of
indoor-outdoor carpeting on the top of the cabinet and
set the saw on it? Would that have any noise dampening
effect?

I doubt it. But I have not tried this before. However, this may not be
a bad idea to use some kind of rubber gasket to seal the gap between
the base of the table saw and the top of the cabinet. Not for noise
reduction, but for avoiding air leaking around the table saw base in
case you surface-mount a dust collection hood on the top of the cabinet
(facing up toward the base of the table saw).
Hope your plan will go well.

Jay Chan