As Skimask says: do you have a pull-up res for MCLR pin in your LED blink circuit? 4K7 is hte commonly used value though higher vals will work with care.
Is your blink circuit power supply good? (With decoupling capacitors where necessary?)
As Squibcakes says: Do you have a dropping/limiting resistor for your LED? 470R to 2K2 should be fine unless you have a superfast 'blink'.

Is it possible to include res+LED etc in your programming circuit to save transferring PIC to the other board? (Just for testing).

If you go the bootloader route I can post a simple transistor circuit for programming via Tx and RX pins. (Easier/cheaper than MAX232 method though obv not true RS232 but it works 100%with the 6 PCs I've tried it with. No guarantees as i don't know how good your soldering is)