I know how anxiety provoking this must be and how difficult it must be to believe your result - my thoughts are with you
I would be cautious with the older test that you fished from the bin - if you didn't get a positive at the time of testing, then the lines that you are now seeing could well be evaporation lines.
The fail safe way to find out if you are pregnant and that this is not a 'chemical pregnancy' where the embryo did not implant properly, is to contact your GP and ask for a referral to the EPU (Early Pregnancy Unit). They will be able to take a blood test which will guage your HCG level. You will, however, have to go back 36-48 hours later for a further blood test so that they can see if the level is rising or not - it should double every 36-48 hours. An alternative but less clear way, would be to start consistantly using the same pregnancy test brand and to see if the result that you get seems to be getting stronger.
When I had a chemical pregnancy/early miscarriage, it took about a week for the HCG to disappear. I would have thought that it would be similar for you if it is a chemical pregnancy, as you will not have developed that much HCG at this stage.
I really hope that the bleeding you saw is implantation and that you have a genuine BFP.