I've just got a couple of Vivitar 283 flashes and a set of DSLRKIT (http://www.ebay.co.uk/itm/110980410870?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1497.l2649) radio triggers. The plan was to have some external flashes which would remote trigger from the NEX 6. The hot-shoe on the NEX 6 is apparently standard so I thought it would just work like on a DSLR.... Has anyone had similar problems with not being able to make the set up work and know a work-around or have I bought a kit that's not compatible?
Have you measured the voltage that your 283 presents? How old are the 283? I have a late 70s vintage 285, and it presents about 350V across the contacts. That worked great with my Nikon F, but will fry a lot of modern electronics. Your flash claims to work to 250V.
You may have fried the triggers--most of these cheap eBay type triggers have a voltage limit of around 300V, and the Vivitar 283s are known to go higher. So, maybe a voltmeter would be worth the investment.
I would also go to the standby advice of check the batteries and the channel settings.
Theoretically, those triggers (which look like they're for Nikon from the pass-through shoe's contact pattern) should work. But if they rely upon a TTL pin signal of some kind, that could be another issue. It's unlikely that this is the case, since those triggers have separate Tx/Rx units, and I've only see this type of misfunction with the Yongnuo RF-603s (which used a TTL signal to auto switch between Tx/Rx modes, so with non-Canon/Nikon hotshoes, the transmitter unit never went into Tx mode--which is why Yongnuo made an RF-603 II).
I've seen reports that the Yongnuo RF-603ii triggers work on NEX (and Fuji X and micro four-thirds), but the sync voltage limit is still only 300V (still better than the 11V limit on the 602s and 603s).