I'm scratching my (sweaty) head with this one.

Last fall I disconnected my A/C unit to accommodate an extension on my house. At the time it was disconnected, everything worked fine.

I reconnected it in its new location. Ran 240V service and a new 18/2 control wire. I connected the control wire just as it was previously. When I turn on the unit from the thermostat everything starts fine but then when the condenser kicks in, the contactor sparks and the condenser stops working. I replace the contactor and nothing changed. I started troubleshooting with a volt meter and found that when the condenser kicks in I get a reading of 100+ volts on the 24V side. I can't find anything shorted out.

Any idea on what might be causing this?

Also, if I hold the contactor in manually the unit runs fine. I'm cooling my house now but there is no thermostat in the loop.

Follow control wiring closely, and especially check out if pulled tight on contactor lug.
If it had 120 present at contactor coil, it will likely need to be replaced. Being a transformer, you may luck out with contactor being a transformer.
You could have outside disconnect Off and turn inside unit on and to Cool. It should put 24 volts out to contactor coil. Verif it pulls contactor down, if not replace.
Then turn on outside disconnect, if it now goes to 120 volts for some strange reason, you know it is from load side of disconnect to compressor and fan.

Follow control wiring closely, and especially check out if pulled tight on contactor lug.
If it had 120 present at contactor coil, it will likely need to be replaced. Being a transformer, you may luck out with contactor being a transformer.
You could have outside disconnect Off and turn inside unit on and to Cool. It should put 24 volts out to contactor coil. Verif it pulls contactor down, if not replace.
Then turn on outside disconnect, if it now goes to 120 volts for some strange reason, you know it is from load side of disconnect to compressor and fan.
Thank you for your reply. I did what you suggested and you are correct. I bypassed the LPS and HPS and went directly to the contactor with 24V and everything seems to work. Except, of course the bypasses switches. I cut the wire ties and searched for a short, separated the wires and made sure that none were touching sheet metal. I then reconnected the 24V properly and got the same result, the contactor sparked when the condenser kicked in. I'm at a loss.

I think you may have looked at the wrong end. It might be coming from the house side.

With the tstat wires disconnected and calling for cooling, measure the voltage to the house side of the unconconnected t-stat wires. Also try measuring voltage from these wires and ground.

Is there a possibiility that Low and high voltage wires were run together in the same conduit?

I think you may have looked at the wrong end. It might be coming from the house side.

with the tstat wires disconnected and calling for cooling, measure the voltage to the house side of the unconconnected t-stat wires. Also try measuring voltage from these wires and ground.

Is there a possibiility that Low and high voltage wires were run together in the same conduit?

The 24V wires have 25.4 volts from the house when disconnected. Both wires from the house are new, 10/3 and 18/2, and do not run together in conduit.

Ok, for the heck of it with the tsat wires disconnected and your probes set to read AC from the coil to ground, operate the coil manually. What do you get?