Let me make sure I understand. When you power up, you can see the word Samsung while it's booting, but then the screen goes black?
Did you attempt to root the phone, or install a new ROM, or anything like that? Did you recently get an update from t-mobile? Are you sure the battery is charged?
If the battery is charged, as a first step, do a battery pull. Leave it out for several minutes, put it back in, and try to boot up again. (This probably won't solve it, but it's worth trying.)
If that doesn't help, then clearing cache as Golfdriver suggest is worth a try. When you boot into recovery, does the screen work normally?
Other than the screen being blank, does the phone seem to work? If someone calls you, does it ring or vibrate? Do notifications work (for example, if you get a text message, does the phone alert you as it normally would)? Or does nothing seem to work at all. If you connect it to a PC, can you see the phone's storage on your PC? For this to work, you'll need the Samsung drivers installed on the PC, and can't use a pattern, pin or password lock.