Illustrated DIY of denso starter

http://www.toyotanation.com/forum/showthread.php?t=319717


Websites that helped me

http://www.camrystuff.com/manuals/Gen4/Starting.pdf
http://www.4crawler.com/4x4/CheapTricks/Starter.shtml
http://www.toyotanation.com/forum/t27312.html

After doing some research on this incident I was convinced that it was definetely the solenoid contacts and plunger (for now).
This is what I bought

Electrical Cleaner Spray - $5.60
Hi Temp Grease - $3.99
Solenoid Plunger - $32.00S
solenoid Contacts both kits $25.00

This is one of the sites that may give you a better price http://www.nationsautoelectric.com/densoparts.html

Click-bzzzz sounds more like a borderline battery. Was it doing this after you replaced the battery? CLICK-CLICK-CLICK-CLICK-start is classic worn contacts. If you don't want to twiddle thumbs, you can yank the starter, pull the contacts, and put the ends next to each other -- worn contacts look like a stairstep, with the eroded part lower than the rest of the contact. If you carefully file down the higher eroded contact so that it matches the height of the lower eroded contact (just the eroded area, not the entire contact), you can eke a bit more time out of those contacts. Not something I recommend long-term, but it's an option. While you've got them out, take a picture of the contacts (different Denso starters have different contacts) and write down the part number of the starter. You might be able to call around to electric motor repair places (or, even better, a place that specializes in starter repair), and score a couple of contacts from there.