A DI box won't boost the level of your signal massively. Some allow for tone shaping (the BDI being one) and some (the one that you've got at the moment) don't have any EQ on them - the tone going into them is the same as the tone coming out.
What a DI box does is to 'balance' the sound to (in theory) eliminate any humming/electronic noise and change the impedance to around 600Ω, which means that the signal can go along ridiculously long cables without any significant loss.
My personal recommendation would be one of these:
http://www.davehallamps.co.uk/page42.html
Really useful EQ section and stupidly low noise units - a bit more expensive than the BDI though.