Networks

Yes, you can have 2 NIC's in a server. You will need to use Network Load Balancing.

A presentation on the subject is linked here:
http://www.jsiinc.com/SUBI/tip4200/rh4295.htm

well, i wouldn't think you would need network load balancing with that small a network but wo details only guessing. have you perused the log on the server to see if you can get clues about what the slowdown is? has it ever worked? does the server have 100mb nics? have you considered throttling them down to 10 to see the effect? is spyware rampant on your network increasing the traffic? are you using an application that runs on MS SQL Desktop? you will not fix it until you understand it imho
consider real server hardware with optimised io for server next time you can buy hardware. also look in mskb at support.microsoft.com for performance optimisation tips

You can use as many nics as your hardware supports, and yes, it is a good idea to attach each nic to another network segment/Switch. If you connect the NICs to the same switch you need, as mentioned above, network load balancing, and that doesn' work with all NICs/ Switches.

Its impossible to say if your solution will solve your problem. It could as well be a misconfiguration of your network or your server, or a damaged protocol. Use network monitor to see if the client access gives an excessive bandwith usage. Monitor also if processor usage is high at the same time. If this is the case, you will notify a slower network if another client needs to contact server resources, and have to investigate if this is normal behaviour for the client action(Most likely it isn't). If this is not the case, there is an internal problem either in your server configuration or your network (hardware?), not solved by adding a second NIC.