You can unplug the OEM alarm - it's a single plug and no harm done. The bike should fire up without it. FWIW, mine was left without the battery for 3 months, stuck and new battery in it and it started on the button, alarm fitted and alarm removed.
So my thoughts are that your battery is still dead. Some will not recharge after being drained completely. I've replaced my old battery with a new one as part of a refurb, but when I went to charge the old one having left it on a shelf for 2months, it took a week of it sat on the optimate to get it to recharge - and I'm still not convinced its actually fully working. Lesson is - if the battery gets dead - just replace it. They are about ?50-70. YTZ10S is the Yuasa code for it.