Its very possible that you cant access your account because you have a Minecraft account rather than a Mojang account. I don't know when, but at some point there was a major system change for Minecraft accounts which meant that a new signup system is now being used. If you used the old system (which is very likely since you cant find your transaction ID) then you can migrate your account to the new system. Also, if you have forgotten the password for the old account it is possible to reset that password via email.
All the info you will need is here: https://account.mojang.com/migrate
I had exactly the same problem very recently and once I got the right account reset everything was OK.
Just seen your earlier post. EnderIO and MFR (MineFactory Reloaded) are both tech mods. They are very nice ones that I would love to have in the pack, but they would not be very high on my priorities list because the majority of what they add is already covered by the mods we have.
If you wanted more tech mods I would suggest:
Extra Utilities: Has similar tech to what we have already, but is very well optimised for reducing lag and server load. The pump, quarry and cobble generator are particularly good examples of this.
Logistics pipes: Expansion to buildcraft pipes that enables high levels of automation, autosorting and autocrafting. People usually use Applied Energistics 2 now but I haven't learnt how that works yet so I've stuck with Logistics pipes
Storage drawers: Blocks that can hold just one to four different items, but many many stacks of them. Left or right clicking on the blocks retrieves or deposits items in and out of them. Integrates very well with other mods thanks to the drawer controller.
I'll stop with the suggestions now before i get too carried away