Just to clarify, when you say your receiver is producing 5V logic levels, you mean that it is sensing the IR signals emitted from the existing remote control?
Is your receiver interfaced to your PIC yet? If not, are you comfortable electrically connecting it to one of the input/output (I/O) ports on the PIC and then reading that port using code?
There are maybe additional ways to look at the data being transmitted by the remote to complement those suggested by other contributors. Could you, for example, write a "data logger" program which does the following (sorry, I haven't got access to the data sheet for the PIC right now so I'm not sure if the exact quantities below are reasonable or not):
1) Configure the I/O port for input from your IR receiver photodiode or whatever
2) Configure an array of, say, 2000 bytes, set to zeroes
3) Construct something like this pseudo code
START
FOR count=0 to 1999
{ read the port data
store the data into array element[count]
wait(1 ms) }
LOOP
Meanwhile, hit a specific button on the remote, aiming it at the receiver
4) Continue in the code...
FOR count=0 to 1999
{ read the array data
print the data element onto the screen (or view the array item in your micro's development environment)
print a space after that }
LOOP
END
Your "logger" should hopefully have captured 2s of port data at 1ms intervals (RAM space permitting), which you'll be able to see on the screen hopefully as a set of ones and zeroes. If you configured your port as an analogue input and used your PIC's analogue to digital converter, these values will be different, but nevertheless you should be able to see distinctly different levels from your IR sensor. You will also be able to tell the period of each logic high level (to the nearest ms), and, possibly, any repeats in the pattern, so you can ignore all but the one burst you need. From there you can do the reverse: distil the periods and levels down to a few byte values, say, and drive an IR LED from one of your output ports, simply by specifying a level and a duration, for each of the button presses you collected data for. Over time and with patience, you can build and encode in your PIC a lookup table of all the codes you want, for any number of remote controls; you'd just read whatever list of codes you need from your collection. There are other, more efficient, ways to encode bit patterns which I'm sure your readers can help with.
A handy thing about the above is that you won't need any additional kit.
Good luck!