DSPIC30f timer1 not trigger everytime on POR
If it only sometimes starts, it is probably a hardware problem.  Check that the power supply rise time is within spec for the PIC.  If not, a external reset circuit may be required.  The power up timer and brown out detect (if there is one) may also help.

It doesn't seem that the firmware is all that relevant to this, but there are a number of issues with it.  Hard coded constant, like 7373, magically picked out of the air are a really bad idea.  Also, your 3-byte increment routine in the interrupt is broken.  It's funny how you have to stand on your head to increment 3 bytes in C when this would be simpler in assembler.  I haven't done a interrupt routine in C30, so I'm not sure about this, but I don't see any obvious way the compiler is supposed to know this is a interrupt routine and therefore end with a RETFIE instruction instead of RETURN.  Isn't there some pragma you have to mutter to the compiler for it to produce a valid interrupt routine?