I am accessing a remote computer using Remote Desktop and want to
print on my local printer. My local printer is an HP PSC 1315. I am
unable to install the printer driver in the remote computer because
the HP 1315 install software tries to detect the printer on the USB of
the remote machine. Is there a way around this? Please respond only if
you have a solution.

Wow the pressure, "please respond ONLY if you have an answer",  

OK for starters you could connect to the remote desktop, run IPCONFIG
/all on the local computer (yours) get your ip address, put that
address on the other (remote) computer (in explorer if you like...)
then you should have access to your printers, as long as you dont have
any firewalls running.

BB

Thanks for your comment. This does not address my problem however,
which is that the remote computer does not have the driver for my
local printer. I cannot install the driver on the remote computer
because the install problem is looking for the same printer to be
connected to the remote USB port.

I have since contacted HP support and they said there is no solution.

I do something very similar to this for my customers. 

These are my assumptions. Let me know what is different.
Your computer and the remote computer are useing Win2k or XP.
You are trying to setup the remote computer to use a networked printer
(not a local printer, i.e. LPT1, LPR, etc.), which is your local
computer's printer.

You are correct that there is currently no native solution in windows
for this driver. As far as I know, this driver needs to attach itself
to a local printer.

This is what you can probably do:
Windows includes an optional component not installed by default called
"Print services for Unix" located in Add/remove programs>>Add/Remove
windows components>>Other Network and File Services>>

This will allow you to  installl the printer LOCALLY on the remote
computer. Yes, locally. Windows will treat this printer as a local
printer instead of a networked one. Consequently, it will let you
manually specify the driver and not try to outsmart you.

At first, it sounds like something you dont want to get in to, but in
reality it is pretty simple. It basically bypasses the whole Windows
printing architechture where Windows thinks it is smarter than you.

There are a couple more steps in configuration, but once you have done
it a couple of times, it is as simple as any other printer
configuration.

Let me know if I am on the right track and I will send you a doc on
the complete setup.

Yes, you are on the right track. I'd greatly appreciate it if you can
send the rest of the instructions.

Put the install cd in the "server" machine (machine you are connecting
to via remote desktop), but do not run the setup wizard that launches
from the CD.  Go to start->settings->printers, and choose to add a
printer.  The add printer wizard will start, when you get to the
question where it asks if it is local or networked printer, choose
local printer and uncheck the autodetect option.  You should be fine
choosing the port as LPT1, even though it is USB, we are not concerned
about the port, just the driver.  The next screen will ask you for the
driver, click on "have disk", and browse the CD for the driver.  It is
hard to tell where the driver is located on the disk, sometimes it is
in the root directory, other times you may have to navigate to
d:\en\drivers\xp\ or similar.  Once you find the .inf on the CD that
corresponds to the driver for your Operating system, you can click Ok,
and the printer driver will be installed.

This should take care of your driver problem, as the driver for your
printer will now be recognized in windows.  You can delete the printer
that you just added, since we are only concerned about the driver.
Choose to KEEP the driver if you are prompted when removing the
printer.

See if it works, if the driver got installed properly on the "server"
it should work.

There is another problem that I have seen with a HP PSC printer that
used a DOT4 printer port on the "client" (machine you are connecting
from); although there is a documented fix for it at:
http://support.microsoft.com/default.aspx?scid=kb;en-us;302361

Let me know how it goes.

Thanks for your help. I got stuck in trying to install the driver. The
disk has 17 *.inf files, including autorun.inf. I tried each one after
choosing "Have Disk" but none allowed me to proceed. No printer showed
up in the Add Printer Wizard after I chose each of the *.inf files. I
am not able to proceed past this step since Windows does not appear to
recognize a printer from the .inf files.

I had a similer problem.

You need to use the stand-alone printer driver that's equilivent to
your PSC Printer.

In this case, it's the HP Deskjet 3420 driver. Download it from the HP
Website, and use that to Install on the server side.

Here's a link to the HP Knowledgebase that will explain it in more detail.

http://h10025.www1.hp.com/ewfrf/wc/document?docname=bpu04830&dlc=en&lc=en&product=412187&lang=en&cc=us&printable=yes&

If you are using 2000 or XP share the printer on the machine that it
is attached. In your case, if I understand what you said, you are
connecting to a remote machine. From the remote machine you are
running a program that you want to print to your machine. If so you
need to share your printer, write down your address, and the drivers
either on your machine or download them to the other machine. From the
remote machine make sure you can get to your machine. Now add a new
printer on the remote machine. Choose local printer attached to this
computer and uncheck automatically check..... On the next screen
choose create a new port and for type of port use the drop down and
select standard TCP/IP port. This will start another wizard. If you
setup a printer name enter it or use the IP address of your machine.
Change the port name if you feel like it. Next choose the printer.
Remember where the drivers are located and choose that inf file.
Complete the rest of the steps. I do this with all USB printer on my
network.