When I turn on the Mitsubishi projection TV, the timer just blinks for a bit, then goes off. The TV never turns on. Any ideas?

Http://www.eserviceinfo.com/index.php?what=search2&searchstring=J52A+(projection)
yes please go to this above website and download the training and troubleshooting manual. if you go through the manual, it will show you what to do and how to do it.
Usually this is a switchmode power supply issue, and it has shut down to prevent a fire, and explosion, or even both. The fault is such that it must not be power on until repaired.
So, it is nearly always my professional opinion that one should always get a "Quote" from the manufacturers recommended service center, Mitsubishi, in your case, please contact a local or head office and ask for a referral to an Authorised service center. Now, I cannot stress how important that last point is. It is even worth the cost of shipping. You see an authorised service agent, will have trained staff, trained on their, your, brand. Also they have first hand access to parts, original parts too. This will actually save you money and ensure you can actually get it back fixed. Of course asking for a "Quote" also gives on the option of repair or replace.

Capacitors on the DM board
1000uf caps, they will be bulged like this
replace with 680uf @ 16volt 105c caps
let me know if you want to dive it, they are solder in parts