My Lilypad w/ATMega328 DOES NOT WORK PLZ HELP

I've bought Arduino Lilypad and USB2Serial board from famous Russian distributor (yeah,I live in Russia, so what?), and I can't upload a sketch to it.
What have I done:
-broke one Lilypad (accidentally)
-found out about the right side of connection for Lylipad and USB2Serial
-read the other topic about Lilypad
-done the advice from other topic
Symptomps
-USB2Serial ON led is flashing, TX and RX DO NOT FLASH (I guess it's the main problem), when I plug in my Lilypad, it's led flashes, flashes more rapidly, then goes out.
-Arduino software does not complete the upload

Also, after a while of trying to burn program to Lilypad, it says: avrdude: stk500_getsync(): not in sync: resp=0x00

Sounds like the bootloader is running on the Lilypad, so I'd say it's problem with USB serial adapter.

What kind of USB serial adapter is it?
Does it have the proper 6-pin FTDI-style header (Gnd,CTS or another GND,Vcc,TX, RX, DTR)?

Have you selected the right serial port from Tools -> Ports?

Do a loopback test on the serial adapter to make sure it's working. You should be able to connect TX and RX of the adapter (no lilypad involved), open serial monitor, send something, and see what you sent appear in the serial monitor. If not, but you've selected the right USB serial adapter, I would suspect problem with serial adapter.

I use standart Arduino FTDI, called USB2SERIAL (photo included(sorry for quality)), and i guess it's pins are ok.

I'm no sure how to do the loopback test. I connected RX and TX on my board, chose the right COM(I check that in Control Panel->System->Hardware->Device Manager-> Ports(Com & LPT)), opened Serial monitor, wrote sth and pressed Enter, and nothing happened.

Did I do the loopback test right, and if yes, does it mean that my FTDI adapter is broken?

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That looks like you did it right (assuming that connector was actually plugged in - it looks like it's fallen out in the picture)... I would suspect problem with the serial adapter.

OK, I'll connect my distributor to change it