There is also two different modems on the market. There is the "SoftModem"
a.k.a. "WinModem" That is software drive. This is a modem that you install
all it's software on the Hard Drive. These can be slow, and unreliable.

Not necessarily. The reliability of soft modems have greatly improved because
of the amount of power that most computers have today.

The resources that softmodems would use when they are operating would be
negligible if it's used in a machine with a clock in excess of 2 GHz with over
512 MB of RAM. In this case, the only limiting factor would be the quality of
the software used to control the modem.
Unfortunately, this is where most softmodems will fall short. Most cheap
brands of softmodems have sloppily written drivers which will affect how well
the modem can communicate and maintain a connection.

Then
there is a Hard Modem. They are the most reliable. These modems have the
software programmed in on the chip of the Modem it's self.

In some cases, yes. In other cases, no.

Again, it depends on the quality of the controlling software that is written.
In the case of a hardware modem, where all modem control processing is handled
by the modem and not by the host CPU, the software instructions in the modem's
ROM chip or firmware can still be sloppily written. Another factor would be
the quality of the chipset.

I forgot to answer this. I wouldn't suspect anything to so with the
computer it's self. See the way how a modem works (I am going to use basic
language here), is a complex language that can be described as different
tones of noise.

What a modem essentially does is MOdulate the information to be sent into a
simple analogue carrier that can be transmitted through the phone lines. The
computer that receives this signal DEModulates it from an analogue carrier back
into usable computer information. It modulates the information to be sent into
a simpler form and then demodulates information it receives back into something
that can be processed, hence the name (MOdulator DEModulator or MODEM for
short).

One big thing, especially on the
older modems, is call waiting. That "Beep" will interrupt the communication
between the two modems. The newer modems comes with a program (sometimes
built into the modem it's self),

If you have call waiting, you can disable it by dialing a turn-off code,
usually *70, at the dial tone prior to dialing out. This is what the modem is
commanded to do if you configure your ISP software to disable call waiting.
Any modem can do this, new or old, as any modem can be told to dial *70 or
whatever the turn-off code is for your area.

In my area, if the turn-off code is successfully received by the switcher at
the phone company, the dial tone will pulse for a couple of seconds to indicate
that call waiting is disabled.

If you hear static on your line when you talk to someone,
the modem will also. This will cause the modem to get confused, and hang
up.

It's not "confusion," per se. Rather, it's noise that interferes with the
carrier. Sometimes, the modem communication can be recovered. Sometimes, it
can't and you have to reconnect.

Make sure you have "Error Correction" enabled on the modem. This will,
sometimes, correct the problem.

Error correction is more meant to correct errors that can occur as the
information is transmitted through the interim. - Reinhart