In answer to your question I would first suggest you have a dicky floppy drive. ( but most likely not ) If you disconnect the floppy drive the machine takes the kinda time you are suggesting to boot. Try an external floppy drive unit, and simply comply with the Commodore Amiga 1200 instruction manual which states that other than a PCMCIA card you cannot plug anything in or switch anything on and off while the machine is hot. That is a golden rule and is why my 1993 Amiga 1200 is still alive. I don`t think its power. Floppy drives can be found on Ebay and my site shows how to fit one.. Could be that something has become a touch loose, like the ribbon to the floppy or the power cable..
One other issue may be shorting out. I had this problem with a couple of cards where the accelerator was causing probs with the shielding. Also press the ROM chips down firmly and check that all the shielding is firmly seated...
AND NOW THE RULE BREAKING BIT...
You can fold the keyboard back on itself resting such that it doesn`t pull the ribbon or wires out and power up with the casing open ( at your risk ) and see if that remedies the problem. If so it is shielding. Sometimes you have to run a strip of insulating tape between the casing and the accelerator where it connects to the motherboard. I have machines with tape and paper in to stop bits touching. Some clever so and so put a reset pin on one mobo that actually touched the shielding with the case closed. Given that you opened the case and put the new ROMs in and installed the Blizzard I would go for poor connection.
By the way... And this is quite dangerous, but can be seen on my website under cardboard Amiga, you can fully remove the motherboard, lay it on a clean flat none metal surface plug in your monitor mouse and keyboard then power and see if she boots... Thats a good way to see if the computer works. Then simply ( with power off ) add each part to see which is causing the problem. ( try doing that with a PC ) I would start with the accelerator. An external floppy drive will be useful. It will take a while to boot without the internal floppy drive. Get SysInfo off Aminet and run that when its working. There really are so few bits to go wrong with the A1200. Also get a brick from an A500. I never have used the original A1200 power supply.. useless... really useless. Also replace the SIMM on the Blizzard.
scuzz
http://www.commodore-amiga-retro.com