Reddit reviews Suzuki SV650 & SV650S '99 to '08 (Haynes Service & Repair Manual)

Reading through some of them comments, your battery it's questionable and in a no start situation is the first thing to rule out.

If you don't have a multimeter, you'll need one for what's going to be required to solve for electrical issues. They're cheap, do you have that going for you. I got the kit from home depot which I've gotten to use on both the bike and in the house. Otherwise, you can get just the multimeter for $20-25. If need be, you can get one at harbor freight for less probably. https://www.homedepot.com/p/Klein-Tools-Electrical-Test-Kit-69149/204367271

https://www.homedepot.com/p/Klein-Tools-Manual-Ranging-Digital-Multimeter-MM300/206517192

You'll want to charge the battery over night to start with. Take it off the charger and get a voltage reading (dc voltage). Wait a few minutes and check again, it should be mostly the same. You can check again in a hour or so if you want but you're looking to verify that the battery holds a charge. If it can't, battery either needs replacing or you've got parasitic drain. Do the leak test to be sure(at bottom) especially if you've made changes to electronics.

If you're still good, crank the bike with the multimeter still on the battery (dc voltage). You might lose a little voltage from cranking but at idle your regulator rectifier should have a you at 13.5-15v and should remain relatively consistent through revving up to 5k rpm (regulated voltage test). If you don't have that voltage at idle or at rev, you're now looking at a charging system issue. Otherwise, you're looking at a starter system issue.

Check these things and report back.

Edit:

To check parasitic drain (leak test). Make sure the bike is off remove the cable(s) from the negative battery terminal. Set your multimeter to amps (start high so you don't blow the fuse) and connect the negative probe from the multimeter to the negative battery terminal. Positive probe from multimeter goes to the cables that were attached to the battery terminal. You'll progressively go to lower amp settings until you get a reading. manual specification for max leakage is .1 mA.

Edit 2

You might consider grabbing a Haynes manual for reference. Not required, but can be helpful to have our next to you while you work.
https://www.amazon.com/gp/aw/d/1785210416/ref=mp_s_a_1_1?ie=UTF8&qid=1517563295&sr=8-1&pi=AC_SX236_SY340_FMwebp_QL65&keywords=Haynes+sv650&dpPl=1&dpID=61hf4RCoDML&ref=plSrch