Sounds like it isn't hooked up right as others said. When asking for help always post photos so we can see what you did. Also post the code you are trying to run. Don't power it up until you get it figured out just in case it still works.
Also I editted your subject so people wouldn't see the title and assume the SRF05 doesn't work with Picaxe when in fact, it does ;)
Sounds like you got a short circuit somewhere.
Check the connections on the SRF05 with the picaxe board. If you read zero ohm between voltage and any of the other pins on the SRF05: thats bad!
Also make sure you connect the wires to the correct pads on the SRF05. The SRF05 has 5 connection pads on each side, but you can only use one row with the picaxe.
If it's not shorted anymore and connected right, a little red light should flash when the SRF05 receives a pulse. If you see the magic little light, it will probable still work.
The pic(axe) can take a lot and I believe the chip on the SRF05 is also a (small) pic. you might be in luck.