You gotta remove that battery before it explodes!!!
I lost two A2000s that way, and many others have too.
If you're handy with a soldering iron you can replace them, but in any case it should be taken off before it starts to swell up and one day you turn it on and it smells funny.
Are there any RAM sticks on your A2091 card? You should be able to fit up to 8MB RAM on there, which would be plenty to turn the A2000 into a useful gaming machine and also perfect for classic applications. I use an A600 with some extra RAM and the stock 7Mhz 68000, and it's a fine computer.
Black & white is no good, you're welcome to have a spare RF Modulator of mine if you like, it plugs into the RGB port and gives you regular colour Composite-out. I have a couple of spares since I use S-Video adapters from
http://amigamaniac.com (an Amiga hardware manufacturer and wholesale seller located in our own state).
I wish I had a spare SCSI hard drive to give you but those things aren't easy to come by. Many people with old SCSI-based Amigas and clasic Macs (who also used SCSI) have had to deal with a lack of SCSI drives for a while, so the arrival of these SCSI smart-card readers in the Mech Ware online shop has really saved a lot of us. It sits inside the second floppy drive bay and lets you insert up to five smart cards at once, and even one of them (at around 4GB anyway) would be plenty big enough to store nearly everything you'd need on the old Amiga.
You could also keep an eye out for a SCSI CD/DVD drive which will work fine on the A2000 with the right filesystem installed (which I can help you with if you decide to do it).