When I try to run my RD-900 Rain Dial sprinkler system, it will run for about 4 minutes then it blows the GFI. I think I might need a new transformer, what do you think?

Transformer, probably not.

Try this:

The system likely has a 24 VAC secondary.

Disconnect the secondary

Either connect two 12 volt automotive bulbs that draw 1-2 amps at 12V about an amp in series to the secondary alone. See if the GFCI pops.

I'm thinking more of an outdoor/underground issue.

A ground fault on the secondary wouln't trip the GFCI.

I have a rain dial rd900 and I can't seem to get it to power up at all?