In Lots_of_serial_outputs.vi, your write loop doesn't wait for the initialization loop. To force write to wait, create data dependency by wiring any output from the initialization loop to the frame of the write loop. You don't need to do anything in the write loop with that output: just wiring it to the frame will force the write loop to wait. Search the LabView help for data dependency for more details.
But that doesn't look like the sole cause of your problem.
You duplicated the problem with Hyperterm, so it's not just a LabView problem.
Sorry: it looks like you have a hardware problem.
You have at least three options:
1. Try another PC.
2. Buy a serial card and install it in the PC. There are a lot of cards for $200 or less. Here are a couple.
htt
p://sine.ni.com/apps/we/nioc.vp?cid=1348〈=US
http://www.quatech.com/shopquatech/products/prod339.asp
http://www.bb-elec.com/product.asp?sku=232PCI2A&dept_id=40
3. Troubleshoot the hardware of your existing PC. Locate the UART chip (probably either a 16550 or a custom chip). Here's the datasheet for the 16550.
http://www.national.com/ds/PC/PC16550D.pdf
If it's a custom chip, you'll need the pinout or the motherboard schematic. Then check for continuity between the chip and the 9 pin connector. E.g., for the 16550, check between SOUT and Transmit Data (pin 3), SIN and Receive Data (pin2), and VSS and Signal Ground (pin 5).